Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
800 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 289 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 |
|---|---|---|
| 2. #5798 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 7. C2×C3×#41 | C4 | semidirect |
| 9. C22×C3×D4 | C4 | semidirect |
| 12. C2×#217 | C22 | semidirect |
| 14. #926 | C22 | semidirect |
| 15. #834 | C22 | semidirect |
| 20. C24×C3 | C2×C4 | semidirect |
| 24. C2×C3×Q8 | C2×C4 | semidirect |
| 28. C2×C3×D4 | C2×C4 | semidirect |
| 29. C2×C3×D4 | C2×C4 | semidirect |
| 32. C22×C3×C4 | C2×C4 | semidirect |
| 33. C22×C3×C4 | C2×C4 | semidirect |
| 41. C2×#41 | Dic3 | semidirect |
| 43. C22×D4 | Dic3 | semidirect |
| 69. C24 | C2×Dic3 | semidirect |
| 73. C2×Q8 | C2×Dic3 | semidirect |
| 77. C2×D4 | C2×Dic3 | semidirect |
| 78. C2×D4 | C2×Dic3 | semidirect |
| 82. C22×C4 | C2×Dic3 | semidirect |
| 83. C22×C4 | C2×Dic3 | semidirect |
| 137. C3 | #2883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| #5798 | 2 |
| #5240 | 2 |
| C2×#834 | 2 |
| #2883 | 3 |