Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 4. C2×#14555520 | C4 | semidirect |
| 9. (C2×#10587739)⋊C4 | C4 | semidirect |
| 13. #17983995 | C4 | semidirect |
| 14. #95×C137 | C4 | semidirect |
| 87. C137 | #1297 | semidirect |
| 102. #95 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578374 | 2 |
| C4×C22⋊#10587739 | 2 |
| #22577250 | 2 |
| #1297 | 137 |