Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 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. #22578139 | C2 | semidirect |
| 3. #22577604 | C2 | semidirect |
| 4. #22577133 | C2 | semidirect |
| 5. #331×C137 | C2 | semidirect |
| 64. C137 | #1620 | semidirect |
| 69. #331 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578139 | 2 |
| #22577779 | 2 |
| #22577604 | 2 |
| #22577133 | 2 |
| #331×C137 | 2 |
| #1620 | 137 |