Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. C2×#808 | C2 | semidirect |
| 5. C2×#807 | C2 | semidirect |
| 6. C3×#340 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 20. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 31. #340 | D3 | semidirect |
| 112. C3⋊C8 | C22⋊C4 | semidirect |
| 232. C3 | #1809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽25) | 2 |
| #4987 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| C3×#340 | 2 |
| #4551 | 2 |
| #1809 | 3 |