Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #5798 | C2 | semidirect |
| 3. #5521 | C2 | semidirect |
| 4. C3×#418 | C2 | semidirect |
| 5. #5131 | C2 | semidirect |
| 6. #5122 | C2 | semidirect |
| 7. #4998 | C2 | semidirect |
| 8. #4785 | C2 | semidirect |
| 9. #4756 | C2 | semidirect |
| 17. D4×Dic3 | C22 | semidirect |
| 18. C2×#213 | C4 | semidirect |
| 24. #893 | C22 | semidirect |
| 27. C3×#102 | C22 | semidirect |
| 28. #821 | C22 | semidirect |
| 29. #815 | C22 | semidirect |
| 30. C8×Dic3 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 32. #807 | C22 | semidirect |
| 40. #418 | D3 | semidirect |
| 46. C2×C3×D4 | C2×C4 | semidirect |
| 52. C2×D12 | C2×C4 | semidirect |
| 63. #213 | C2×C4 | semidirect |
| 64. #213 | C2×C4 | semidirect |
| 70. C2×C3⋊C8 | C2×C4 | semidirect |
| 92. #102 | C2×D3 | semidirect |
| 128. C2×D4 | C4×D3 | semidirect |
| 211. C3 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5798 | 2 |
| C22×#213 | 2 |
| #5521 | 2 |
| C3×#418 | 2 |
| #5131 | 2 |
| #5122 | 2 |
| #4998 | 2 |
| #4785 | 2 |
| #4756 | 2 |
| #2948 | 3 |