Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. #22578123 | C2 | semidirect |
| 2. #22577750 | C2 | semidirect |
| 3. #22577604 | C2 | semidirect |
| 5. #22577148 | C2 | semidirect |
| 6. #22577135 | C2 | semidirect |
| 7. D4⋊C8×C137 | C2 | semidirect |
| 95. C137 | #1628 | semidirect |
| 103. D4⋊C8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578123 | 2 |
| #22577750 | 2 |
| #22577604 | 2 |
| #22577598 | 2 |
| #22577148 | 2 |
| #22577135 | 2 |
| D4⋊C8×C137 | 2 |
| #1628 | 137 |