Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #22577511 | C2 | semidirect |
| 3. #22577227 | C2 | semidirect |
| 4. #22577218 | C2 | semidirect |
| 6. #22577181 | C2 | semidirect |
| 10. #17984034 | C4 | semidirect |
| 11. #17984032 | C4 | semidirect |
| 64. C137 | #2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577843 | 2 |
| #22577511 | 2 |
| #22577227 | 2 |
| #22577218 | 2 |
| #22577213 | 2 |
| #22577181 | 2 |
| #444×C137 | 2 |
| #2180 | 137 |