Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22577953 | C2 | semidirect |
| 2. #22577716 | C2 | semidirect |
| 3. #22577683 | C2 | semidirect |
| 4. #22577598 | C2 | semidirect |
| 5. #22577537 | C2 | semidirect |
| 6. C4×#14555495 | C2 | semidirect |
| 7. #22577456 | C2 | semidirect |
| 8. C2×C4×D4×C137 | C2 | semidirect |
| 11. #17984088 | C22 | semidirect |
| 12. #17984085 | C22 | semidirect |
| 17. C4×D548 | C22 | semidirect |
| 18. #17984021 | C22 | semidirect |
| 19. C4⋊#11764040 | C22 | semidirect |
| 21. #17984008 | C22 | semidirect |
| 23. C4×#11764040 | C22 | semidirect |
| 81. D4×C137 | #41 | semidirect |
| 88. C2×C4×C137 | D8 | semidirect |
| 120. C137 | #3100 | semidirect |
| 123. C2×C4×D4 | D137 | semidirect |
| 199. D4 | #14555510 | semidirect |
| 208. C2×C4 | #14555495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577953 | 2 |
| #22577716 | 2 |
| #22577683 | 2 |
| #22577598 | 2 |
| #22577537 | 2 |
| C4×#14555495 | 2 |
| #22577456 | 2 |
| C2×C4×D4×C137 | 2 |
| #3100 | 137 |