Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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×C32×C8 | C2 | semidirect |
| 2. #64139 | C2 | semidirect |
| 3. C2×#3745 | C2 | semidirect |
| 4. #63648 | C2 | semidirect |
| 5. #63645 | C2 | semidirect |
| 16. C22×C3×C8 | D3 | semidirect |
| 32. C32×C8 | D4 | semidirect |
| 45. C22×C32 | D8 | semidirect |
| 55. C22×C8 | C3⋊D3 | semidirect |
| 70. C3×C8 | #67 | semidirect |
| 87. C22×C3 | D24 | semidirect |
| 96. C32 | #466 | semidirect |
| 108. C8 | #638 | semidirect |
| 119. C22 | #3745 | semidirect |
| 125. C3 | #5115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C8 | 2 |
| #64139 | 2 |
| C2×#3745 | 2 |
| #63648 | 2 |
| #63645 | 2 |
| #5115 | 3 |