Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C3×C4⋊Q8 | C2 |
| prime radical | C2×D12 | C22 |
| hypercenter | C4⋊Q8 | D3 |
| hypocenter | C3 | D4×Q8 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D3×Q8 | C2 | semidirect |
| 2. C3×C4⋊Q8 | C2 | semidirect |
| 3. #946 | C2 | semidirect |
| 4. #896 | C2 | semidirect |
| 6. #888 | C2 | semidirect |
| 8. C4×Dic6 | C2 | semidirect |
| 29. C4⋊Q8 | D3 | semidirect |
| 44. D12 | Q8 | semidirect |
| 48. Dic6 | D4 | semidirect |
| 69. C2×D3 | C2×Q8 | semidirect |
| 73. C3×C4 | C2×Q8 | semidirect |
| 105. C4 | D3×Q8 | semidirect |
| 106. C3 | D4×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C3×C4⋊Q8 | 2 |
| #946 | 2 |
| #896 | 2 |
| #893 | 2 |
| #888 | 2 |
| C4×D12 | 2 |
| C4×Dic6 | 2 |
| D4×Q8 | 3 |