Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22577821 | C2 | semidirect |
| 3. #22577188 | C2 | semidirect |
| 4. C4×#14555485 | C2 | semidirect |
| 5. #364×C137 | C2 | semidirect |
| 50. C137 | #2170 | semidirect |
| 54. #364 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577821 | 2 |
| #22577521 | 2 |
| #22577188 | 2 |
| C4×#14555485 | 2 |
| #364×C137 | 2 |
| #2170 | 137 |