Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×D4 |
| commutator, cosocle | C2×C3×C4 | C23 |
| Frattini | C2×C4 | C22×D3 |
| Fitting | C2×C3×D8 | C2 |
| socle | C22×C3 | C2×D4 |
| hypercenter | C2×D8 | D3 |
| hypocenter | C3 | #449 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#237 | C2 | semidirect |
| 2. C2×C3×D8 | C2 | semidirect |
| 3. #938 | C2 | semidirect |
| 4. C2×#214 | C2 | semidirect |
| 5. #832 | C2 | semidirect |
| 6. (C2×D3)⋊C8 | C2 | semidirect |
| 7. #816 | C2 | semidirect |
| 26. C2×D8 | D3 | semidirect |
| 37. C3×D4 | D4 | semidirect |
| 48. Dic6 | D4 | semidirect |
| 91. D4 | #67 | semidirect |
| 122. C3 | #449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C2×C3×D8 | 2 |
| #938 | 2 |
| C2×#214 | 2 |
| #832 | 2 |
| (C2×D3)⋊C8 | 2 |
| #816 | 2 |
| #449 | 3 |