Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22577231 | C2 | semidirect |
| 5. #22577230 | C2 | semidirect |
| 6. #22577228 | C2 | semidirect |
| 7. #366×C137 | C2 | semidirect |
| 11. #17984027 | C4 | semidirect |
| 30. #14555485 | C2×C4 | semidirect |
| 34. C16×C137 | C2×C4 | semidirect |
| 63. C137 | #2159 | semidirect |
| 71. #366 | D137 | semidirect |
| 98. C16 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984027 | 2 |
| #22577440 | 2 |
| #107×D137 | 2 |
| #22577231 | 2 |
| #22577230 | 2 |
| #22577228 | 2 |
| #366×C137 | 2 |
| #2159 | 137 |