Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22577749 | C2 | semidirect |
| 3. #22577684 | C2 | semidirect |
| 4. #22577609 | C2 | semidirect |
| 5. #22577130 | C2 | semidirect |
| 6. #22577130 | C2 | semidirect |
| 7. #331×C137 | C2 | semidirect |
| 11. #17984088 | C22 | semidirect |
| 21. C4×#11764040 | C22 | semidirect |
| 23. C4⋊C8×C137 | C22 | semidirect |
| 24. C4⋊C8×C137 | C22 | semidirect |
| 62. D548 | SD16 | semidirect |
| 109. C137 | #1639 | semidirect |
| 115. #331 | D137 | semidirect |
| 129. C4⋊C8 | C2×D137 | semidirect |
| 130. C4⋊C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578038 | 2 |
| #22577749 | 2 |
| #22577684 | 2 |
| #22577609 | 2 |
| #22577130 | 2 |
| #331×C137 | 2 |
| #1639 | 137 |