Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #30660368 | C2 | semidirect |
| 2. #30660364 | C2 | semidirect |
| 3. #30660362 | C2 | semidirect |
| 4. #30660357 | C2 | semidirect |
| 6. Q8×Dic523 | C2 | semidirect |
| 7. #30660335 | C2 | semidirect |
| 8. (C22⋊D523)⋊C4 | C2 | semidirect |
| 9. #30660331 | C2 | semidirect |
| 10. C2×C4×Dic523 | C2 | semidirect |
| 11. C22⋊Q8×C523 | C2 | semidirect |
| 74. C523 | #529 | semidirect |
| 80. C22⋊Q8 | D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660368 | 2 |
| #30660364 | 2 |
| #30660362 | 2 |
| #30660357 | 2 |
| #30660347 | 2 |
| Q8×Dic523 | 2 |
| #30660335 | 2 |
| (C22⋊D523)⋊C4 | 2 |
| #30660331 | 2 |
| C2×C4×Dic523 | 2 |
| C22⋊Q8×C523 | 2 |
| #529 | 523 |