Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14555497 | C2 | semidirect |
| 2. C2×#17984095 | C2 | semidirect |
| 4. #22577651 | C2 | semidirect |
| 5. #22577634 | C2 | semidirect |
| 6. #22577439 | C2 | semidirect |
| 7. #22577412 | C2 | semidirect |
| 8. #22577407 | C2 | semidirect |
| 9. #536×C137 | C2 | semidirect |
| 16. C2×#14555494 | C22 | semidirect |
| 18. C22×#11764040 | C22 | semidirect |
| 24. #17984021 | C22 | semidirect |
| 25. #17984019 | C22 | semidirect |
| 26. #17984012 | C22 | semidirect |
| 33. C22⋊Q8×C137 | C22 | semidirect |
| 46. C2×#11764040 | D4 | semidirect |
| 120. C137 | #3057 | semidirect |
| 124. #536 | D137 | semidirect |
| 147. C22⋊Q8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| C2×#17984095 | 2 |
| #22577967 | 2 |
| #22577651 | 2 |
| #22577634 | 2 |
| #22577439 | 2 |
| #22577412 | 2 |
| #22577407 | 2 |
| #536×C137 | 2 |
| #3057 | 137 |