Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #953 |
| commutator, cosocle | C22×C3×C4 | C23 |
| Frattini | C22×C4 | C22×D3 |
| Fitting | C3×#535 | C2 |
| socle | C22×C3 | #120 |
| hypercenter | #535 | D3 |
| hypocenter | C3 | #2002 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#535 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C2×#940 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. C2×#833 | C2 | semidirect |
| 6. #5001 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 31. #535 | D3 | semidirect |
| 43. C2×C3×Q8 | D4 | semidirect |
| 52. C2×C3×D4 | D4 | semidirect |
| 63. C2×D12 | D4 | semidirect |
| 64. C3×C4⋊C4 | D4 | semidirect |
| 71. C4×Dic3 | D4 | semidirect |
| 75. #208 | D4 | semidirect |
| 145. C2×Q8 | #67 | semidirect |
| 162. C2×D4 | #67 | 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 |
|---|---|
| C3×#535 | 2 |
| C2×#949 | 2 |
| C2×#940 | 2 |
| C2×#837 | 2 |
| C2×#833 | 2 |
| #5001 | 2 |
| #4532 | 2 |
| #2002 | 3 |