Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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. C2×#22552629 | C2 | semidirect |
| 2. C2×#22552624 | C2 | semidirect |
| 3. #30660353 | C2 | semidirect |
| 5. #30660306 | C2 | semidirect |
| 6. #30660298 | C2 | semidirect |
| 7. #102×C523 | C2 | semidirect |
| 30. C523⋊C8 | D4 | semidirect |
| 55. C523 | #468 | semidirect |
| 63. #102 | D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552629 | 2 |
| C2×#22552624 | 2 |
| #30660353 | 2 |
| #30660344 | 2 |
| #30660306 | 2 |
| #30660298 | 2 |
| #102×C523 | 2 |
| #468 | 523 |