Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D3 |
| commutator, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting | C2×C3×C22⋊C4 | C2 |
| socle | C23×C3 | C23 |
| hypercenter | C2×C22⋊C4 | D3 |
| hypocenter | C3 | C2×#120 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D3 | C2 | semidirect |
| 2. C22×#67 | C2 | semidirect |
| 3. C22×D12 | C2 | semidirect |
| 4. C2×C3×C22⋊C4 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #882 | C2 | direct (N × H) |
| 12. C23×D3 | C22 | semidirect |
| 13. C23×D3 | C22 | semidirect |
| 14. C22×C3×C4 | C22 | semidirect |
| 16. C2×#67 | C22 | semidirect |
| 17. C22×Dic3 | C22 | semidirect |
| 19. C2×D12 | C22 | semidirect |
| 20. C3×C22⋊C4 | C22 | semidirect |
| 21. (C2×D3)⋊C4 | C22 | semidirect |
| 27. C2×C22⋊C4 | D3 | semidirect |
| 29. C23×C3 | D4 | semidirect |
| 39. C22×D3 | D4 | semidirect |
| 41. C22×D3 | C23 | semidirect |
| 43. C2×C3×C4 | C23 | semidirect |
| 46. C2×Dic3 | C23 | semidirect |
| 59. C22×C4 | C2×D3 | semidirect |
| 61. C22⋊C4 | C2×D3 | semidirect |
| 66. C22×C3 | C2×D4 | semidirect |
| 75. C2×D3 | C2×D4 | semidirect |
| 89. C23 | D12 | semidirect |
| 97. C2×C4 | C22×D3 | semidirect |
| 99. C2×C3 | #120 | semidirect |
| 115. C22 | C2×D12 | semidirect |
| 120. C3 | C2×#120 | semidirect |
| 124. C2 | #882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D3 | 2 |
| C22×#67 | 2 |
| C22×D12 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| #882 | 2 |
| C2×#120 | 3 |