Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
402 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 144 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. #22578438 | C2 | semidirect |
| 2. #22578436 | C2 | semidirect |
| 3. #22578434 | C2 | semidirect |
| 4. #22578432 | C2 | semidirect |
| 5. #22578428 | C2 | semidirect |
| 6. #22578376 | C2 | semidirect |
| 7. #22578375 | C2 | semidirect |
| 8. #22578374 | C2 | semidirect |
| 12. C2×#14555519 | C22 | semidirect |
| 13. C22×#11764047 | C22 | semidirect |
| 14. #17984155 | C22 | semidirect |
| 15. C4⋊#11764047 | C22 | semidirect |
| 22. C22⋊#11764047 | C22 | semidirect |
| 23. C22⋊#11764047 | C22 | semidirect |
| 24. #17984143 | C22 | semidirect |
| 25. C4×#11764047 | C22 | semidirect |
| 129. C137 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578438 | 2 |
| #22578436 | 2 |
| #22578434 | 2 |
| #22578432 | 2 |
| #22578428 | 2 |
| #22578376 | 2 |
| #22578375 | 2 |
| #22578374 | 2 |
| #22577913 | 2 |
| #2978 | 137 |