Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22578058 | C2 | semidirect |
| 2. #22577755 | C2 | semidirect |
| 3. #22577744 | C2 | semidirect |
| 4. #22577690 | C2 | semidirect |
| 5. #22577630 | C2 | semidirect |
| 6. #22577608 | C2 | semidirect |
| 7. #22577546 | C2 | semidirect |
| 8. C4×#14555495 | C2 | semidirect |
| 9. D4×#11764040 | C2 | semidirect |
| 10. #22577397 | C2 | semidirect |
| 11. #555×C137 | C2 | semidirect |
| 130. C137 | #3303 | semidirect |
| 132. #555 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578058 | 2 |
| #22577755 | 2 |
| #22577744 | 2 |
| #22577690 | 2 |
| #22577630 | 2 |
| #22577608 | 2 |
| #22577546 | 2 |
| C4×#14555495 | 2 |
| D4×#11764040 | 2 |
| #22577397 | 2 |
| #555×C137 | 2 |
| #3303 | 137 |