Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22577808 | C2 | semidirect |
| 4. #22577613 | C2 | semidirect |
| 5. #22577148 | C2 | semidirect |
| 7. Q8⋊C8×C137 | C2 | semidirect |
| 57. D548 | Q16 | semidirect |
| 92. C137 | #1649 | semidirect |
| 99. Q8⋊C8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D548 | 2 |
| #22577808 | 2 |
| #22577684 | 2 |
| #22577613 | 2 |
| #22577148 | 2 |
| #22577132 | 2 |
| Q8⋊C8×C137 | 2 |
| #1649 | 137 |