Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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. #22578410 | C2 | semidirect |
| 4. C2×#17984142 | C2 | semidirect |
| 5. #22578279 | C2 | semidirect |
| 6. #22578273 | C2 | semidirect |
| 21. #17984013 | C4 | semidirect |
| 22. #17984011 | C4 | semidirect |
| 23. #17984009 | C4 | semidirect |
| 24. #102×C137 | C4 | semidirect |
| 105. C137 | #1938 | semidirect |
| 127. #102 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578410 | 2 |
| C2×#17984152 | 2 |
| #22578377 | 2 |
| C2×#17984142 | 2 |
| #22578279 | 2 |
| #22578273 | 2 |
| #22577396 | 2 |
| #1938 | 137 |