Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. #17983998 | C4 | semidirect |
| 52. #11764040 | C4⋊C4 | semidirect |
| 64. C8×C137 | C4⋊C4 | semidirect |
| 84. C137 | #1847 | semidirect |
| 149. C8 | #14555489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984021 | 2 |
| C2×#17984020 | 2 |
| C2×#17984019 | 2 |
| C2×#17983998 | 2 |
| #22577272 | 2 |
| #22577268 | 2 |
| C2×#107×C137 | 2 |
| #1847 | 137 |