Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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. #30660366 | C2 | semidirect |
| 3. #30660363 | C2 | semidirect |
| 4. #30660363 | C2 | semidirect |
| 5. #30660358 | C2 | semidirect |
| 6. #30660356 | C2 | semidirect |
| 7. #30660355 | C2 | semidirect |
| 8. #30660355 | C2 | semidirect |
| 9. #30660349 | C2 | semidirect |
| 10. #30660349 | C2 | semidirect |
| 12. #30660335 | C2 | semidirect |
| 13. C4×C22⋊D523 | C2 | semidirect |
| 14. C4⋊C4×D523 | C2 | semidirect |
| 15. C22⋊Q8×C523 | C2 | semidirect |
| 103. C523 | #539 | semidirect |
| 115. 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 |
| #30660366 | 2 |
| #30660363 | 2 |
| #30660358 | 2 |
| #30660356 | 2 |
| #30660355 | 2 |
| #30660349 | 2 |
| #30660346 | 2 |
| #30660335 | 2 |
| C4×C22⋊D523 | 2 |
| C4⋊C4×D523 | 2 |
| C22⋊Q8×C523 | 2 |
| #539 | 523 |