Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22577801 | C2 | semidirect |
| 5. #22577151 | C2 | semidirect |
| 6. #22577150 | C2 | semidirect |
| 7. #334×C137 | C2 | semidirect |
| 59. C8×C137 | SD16 | semidirect |
| 76. C137 | #1671 | semidirect |
| 82. #334 | D137 | semidirect |
| 136. C8 | #14555499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577801 | 2 |
| #22577694 | 2 |
| #22577609 | 2 |
| C8×D548 | 2 |
| #22577151 | 2 |
| #22577150 | 2 |
| #334×C137 | 2 |
| #1671 | 137 |