Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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. #4683 | C2 | semidirect |
| 5. #4490 | C2 | semidirect |
| 6. #4489 | C2 | semidirect |
| 7. C4⋊(C3⋊C16) | C2 | semidirect |
| 120. C3 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| #4683 | 2 |
| #4562 | 2 |
| #4490 | 2 |
| #4489 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2228 | 3 |