Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
578 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C3×#99 | C2 | semidirect |
| 4. #4955 | C2 | semidirect |
| 5. #4527 | C2 | semidirect |
| 15. #937 | C4 | semidirect |
| 23. C2×#99 | D3 | semidirect |
| 33. C23×D3 | C2×C4 | semidirect |
| 44. C22×Dic3 | D4 | semidirect |
| 51. #217 | C2×C4 | semidirect |
| 74. C23×C3 | C22⋊C4 | semidirect |
| 98. C2×C3×C4 | C22⋊C4 | semidirect |
| 177. C23 | (C2×D3)⋊C4 | semidirect |
| 195. C2×C4 | (C2×D3)⋊C4 | semidirect |
| 230. C3 | #1889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#937 | 2 |
| #5798 | 2 |
| C2×C3×#99 | 2 |
| #4955 | 2 |
| #4527 | 2 |
| #1889 | 3 |