Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984116 | C2 | semidirect |
| 2. C2×#17984085 | C2 | semidirect |
| 3. C4×#14555510 | C2 | semidirect |
| 4. #22577604 | C2 | semidirect |
| 5. #22577599 | C2 | semidirect |
| 6. #22577409 | C2 | semidirect |
| 7. #423×C137 | C2 | semidirect |
| 12. C2×#14555499 | C22 | semidirect |
| 13. C2×D1096 | C22 | semidirect |
| 17. C4×Dic274 | C22 | semidirect |
| 18. C4×D548 | C22 | semidirect |
| 23. #17984010 | C22 | semidirect |
| 26. C4⋊C8×C137 | C22 | semidirect |
| 29. #14555510 | D4 | semidirect |
| 62. Dic274 | C2×D4 | semidirect |
| 69. D548 | C2×D4 | semidirect |
| 94. C4×C137 | AGL(1,ℤ/8) | semidirect |
| 104. C137 | #3038 | semidirect |
| 111. #423 | D137 | semidirect |
| 130. C4⋊C8 | C2×D137 | semidirect |
| 201. C4 | #17984116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984116 | 2 |
| C2×#17984085 | 2 |
| C4×#14555510 | 2 |
| #22577604 | 2 |
| #22577599 | 2 |
| #22577409 | 2 |
| #423×C137 | 2 |
| #3038 | 137 |