Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C2×#3711 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 32. #830 | D3 | semidirect |
| 51. C3⋊(C3⋊C8) | D4 | semidirect |
| 87. C22×C32 | M16 | semidirect |
| 173. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 174. C22×C3 | #208 | semidirect |
| 195. C32 | #435 | semidirect |
| 231. C22 | #3711 | semidirect |
| 240. C3 | #4730 | semidirect |
| 241. C3 | #5011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C8) | 2 |
| C3×C4×#67 | 2 |
| C2×#3711 | 2 |
| C3×#830 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #63554 | 2 |
| #5011 | 3 |
| #4730 | 3 |