Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5570 | C2 | semidirect |
| 5. #5060 | C2 | semidirect |
| 6. #5054 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. C4×#216 | C2 | semidirect |
| 9. #5024 | C2 | semidirect |
| 10. #5019 | C2 | semidirect |
| 11. #5018 | C2 | semidirect |
| 238. C3 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#559 | 2 |
| #5570 | 2 |
| #5076 | 2 |
| #5075 | 2 |
| #5060 | 2 |
| #5054 | 2 |
| #5031 | 2 |
| C4×#216 | 2 |
| #5024 | 2 |
| #5019 | 2 |
| #5018 | 2 |
| #3400 | 3 |