Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22577690 | C2 | semidirect |
| 3. #22577482 | C2 | semidirect |
| 4. #22577156 | C2 | semidirect |
| 5. #22577152 | C2 | semidirect |
| 6. #22577147 | C2 | semidirect |
| 7. #486×C137 | C2 | semidirect |
| 82. C137 | #1697 | semidirect |
| 84. #486 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577690 | 2 |
| #22577595 | 2 |
| #22577482 | 2 |
| #22577156 | 2 |
| #22577152 | 2 |
| #22577147 | 2 |
| #486×C137 | 2 |
| #1697 | 137 |