Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
464 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 213 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. #22577310 | C2 | semidirect |
| 2. #22577302 | C2 | semidirect |
| 5. #22577289 | C2 | semidirect |
| 6. #22577289 | C2 | semidirect |
| 28. C22⋊Q8×C137 | C4 | semidirect |
| 110. C137 | #2378 | semidirect |
| 123. C22⋊Q8 | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577310 | 2 |
| #22577302 | 2 |
| #22577296 | 2 |
| #22577289 | 2 |
| #22577266 | 2 |
| #22577263 | 2 |
| C2×C22⋊Q8×C137 | 2 |
| #2378 | 137 |