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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#127 | C2 | semidirect |
| 2. #5805 | C2 | semidirect |
| 3. C2×#932 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. C2×#805 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 32. C2×#127 | D3 | semidirect |
| 52. C2×C3×D4 | D4 | semidirect |
| 61. C2×D12 | D4 | semidirect |
| 63. C2×Dic6 | D4 | semidirect |
| 65. C3×C42 | D4 | semidirect |
| 70. C4⋊Dic3 | D4 | semidirect |
| 75. #208 | D4 | semidirect |
| 162. C2×D4 | #67 | semidirect |
| 179. C42 | #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×C3×#127 | 2 |
| #5805 | 2 |
| C2×#932 | 2 |
| C2×#833 | 2 |
| #5215 | 2 |
| C2×#805 | 2 |
| #4523 | 2 |
| #2002 | 3 |