Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
588 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5240 | C2 | semidirect |
| 3. #5237 | C2 | semidirect |
| 4. #5236 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 10. C2×C3×#41 | C4 | semidirect |
| 15. C22×C3×D4 | C4 | semidirect |
| 17. #926 | C22 | semidirect |
| 18. C2×#208 | C22 | semidirect |
| 67. C2×#41 | Dic3 | semidirect |
| 72. C22×D4 | Dic3 | semidirect |
| 222. C3 | #1795 | 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 |
| #5240 | 2 |
| #5237 | 2 |
| #5236 | 2 |
| #5215 | 2 |
| #1795 | 3 |