Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #22578418 | C2 | semidirect |
| 4. M16×#10587739 | C2 | semidirect |
| 5. #22578286 | C2 | semidirect |
| 6. #22578275 | C2 | semidirect |
| 23. #17984006 | C4 | semidirect |
| 24. #17984006 | C4 | semidirect |
| 25. #17984005 | C4 | semidirect |
| 26. #100×C137 | C4 | semidirect |
| 105. C137 | #1932 | semidirect |
| 130. #100 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578418 | 2 |
| #22578401 | 2 |
| C2×#17984152 | 2 |
| M16×#10587739 | 2 |
| #22578286 | 2 |
| #22578275 | 2 |
| #22577384 | 2 |
| #1932 | 137 |