Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 15. #17984019 | C4 | semidirect |
| 59. #11764040 | C4⋊C4 | semidirect |
| 98. C137 | #1944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984021 | 2 |
| C2×#17984019 | 2 |
| C2×#17983998 | 2 |
| #22577302 | 2 |
| #22577299 | 2 |
| #22577166 | 2 |
| #340×C137 | 2 |
| #1944 | 137 |