Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #937 |
| commutator, cosocle | C22×C3×C4 | C23 |
| Frattini | C22×C4 | C22×D3 |
| Fitting | C3×#418 | C2 |
| socle | C22×C3 | #120 |
| hypercenter | #418 | D3 |
| hypocenter | C3 | #2002 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #418 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#940 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. #5525 | C2 | semidirect |
| 4. C3×#418 | C2 | semidirect |
| 5. C2×#825 | C2 | semidirect |
| 6. C2×#823 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 34. #418 | D3 | semidirect |
| 44. C2×C3×D4 | D4 | semidirect |
| 61. C2×D12 | D4 | semidirect |
| 63. C2×Dic6 | D4 | semidirect |
| 67. C3×C4⋊C4 | D4 | semidirect |
| 74. C4×Dic3 | D4 | semidirect |
| 76. #208 | D4 | semidirect |
| 162. C2×D4 | D12 | semidirect |
| 174. C4⋊C4 | #67 | semidirect |
| 269. C3 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| C2×#932 | 2 |
| #5525 | 2 |
| C3×#418 | 2 |
| C2×#825 | 2 |
| C2×#823 | 2 |
| #4532 | 2 |
| #2002 | 3 |