Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
362 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. C2×#17984157 | C2 | semidirect |
| 4. #22578354 | C2 | semidirect |
| 5. #22578276 | C2 | semidirect |
| 6. #22578268 | C2 | semidirect |
| 23. #17984010 | C4 | semidirect |
| 24. #17984009 | C4 | semidirect |
| 25. #17984008 | C4 | semidirect |
| 26. #102×C137 | C4 | semidirect |
| 54. C2×#11764040 | C2×C4 | semidirect |
| 57. C4⋊Dic137 | C2×C4 | semidirect |
| 60. C2×C8×C137 | C2×C4 | semidirect |
| 61. C4⋊C4×C137 | C2×C4 | semidirect |
| 85. D548 | C4⋊C4 | semidirect |
| 99. D4×C137 | C4⋊C4 | semidirect |
| 139. C137 | #1862 | semidirect |
| 165. #102 | #10587739 | semidirect |
| 190. C2×C8 | C2×#10587739 | semidirect |
| 198. C4⋊C4 | C2×#10587739 | semidirect |
| 216. D4 | C4⋊#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10587739 | 2 |
| C2×#17984157 | 2 |
| C2×#17984150 | 2 |
| #22578354 | 2 |
| #22578276 | 2 |
| #22578268 | 2 |
| #102×D137 | 2 |
| #1862 | 137 |