Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 154 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. #22578428 | C2 | semidirect |
| 2. #22578427 | C2 | semidirect |
| 3. #22578408 | C2 | semidirect |
| 4. #22578407 | C2 | semidirect |
| 6. C4×#14555520 | C2 | semidirect |
| 10. #17984155 | C22 | semidirect |
| 11. C4⋊#11764047 | C22 | semidirect |
| 14. #17984143 | C22 | semidirect |
| 15. C4×#11764047 | C22 | semidirect |
| 104. C137 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578428 | 2 |
| #22578427 | 2 |
| #22578408 | 2 |
| #22578407 | 2 |
| #22578374 | 2 |
| C4×#14555520 | 2 |
| #117×D137 | 2 |
| #2921 | 137 |