Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C3×#107 | C2 | semidirect |
| 3. C2×#817 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 15. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 20. C2×#107 | D3 | semidirect |
| 84. C3×C8 | C22⋊C4 | semidirect |
| 152. C8 | (C2×D3)⋊C4 | semidirect |
| 176. 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 |
| C2×C3×#107 | 2 |
| C2×#817 | 2 |
| #4987 | 2 |
| #4529 | 2 |
| #1809 | 3 |