Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #22577411 | C2 | semidirect |
| 5. C2×#17984006 | C2 | semidirect |
| 6. #22577161 | C2 | semidirect |
| 7. #344×C137 | C2 | semidirect |
| 12. C2×Dic548 | C4 | semidirect |
| 13. C2×#14555499 | C4 | semidirect |
| 107. C137 | #1902 | semidirect |
| 114. #344 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| #22578169 | 2 |
| #22577421 | 2 |
| #22577411 | 2 |
| C2×#17984006 | 2 |
| #22577161 | 2 |
| #344×C137 | 2 |
| #1902 | 137 |