Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #22577482 | C2 | semidirect |
| 3. #22577480 | C2 | semidirect |
| 4. #22577456 | C2 | semidirect |
| 5. #22577365 | C2 | semidirect |
| 6. #431×C137 | C2 | semidirect |
| 9. C2×#14555493 | C22 | semidirect |
| 16. C4⋊#11764040 | C22 | semidirect |
| 18. #17984000 | C22 | semidirect |
| 19. C4×#11764040 | C22 | semidirect |
| 21. C4⋊C8×C137 | C22 | semidirect |
| 23. C4×C8×C137 | C22 | semidirect |
| 60. C2×C4×C137 | M16 | semidirect |
| 88. C137 | #2975 | semidirect |
| 94. #431 | D137 | semidirect |
| 107. C4⋊C8 | C2×D137 | semidirect |
| 112. C4×C8 | C2×D137 | semidirect |
| 148. C2×C4 | #14555493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D548 | 2 |
| #22577482 | 2 |
| #22577480 | 2 |
| #22577456 | 2 |
| #22577365 | 2 |
| #431×C137 | 2 |
| #2975 | 137 |