Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22578034 | C2 | semidirect |
| 3. #22577713 | C2 | semidirect |
| 4. #22577702 | C2 | semidirect |
| 5. #22577692 | C2 | semidirect |
| 6. #22577687 | C2 | semidirect |
| 7. #22577443 | C2 | semidirect |
| 8. #22577429 | C2 | semidirect |
| 11. C2×#106×C137 | C2 | semidirect |
| 42. #14555510 | Q8 | semidirect |
| 123. C137 | #3084 | semidirect |
| 132. C2×#106 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578034 | 2 |
| #22577884 | 2 |
| #22577713 | 2 |
| #22577702 | 2 |
| #22577692 | 2 |
| #22577687 | 2 |
| #22577443 | 2 |
| #22577429 | 2 |
| #22577402 | 2 |
| #22577400 | 2 |
| C2×#106×C137 | 2 |
| #3084 | 137 |