Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984136 | C2 | semidirect |
| 2. C2×#17984116 | C2 | semidirect |
| 3. C22×#14555497 | C2 | semidirect |
| 4. #22577972 | C2 | semidirect |
| 5. #22577551 | C2 | semidirect |
| 6. #22577543 | C2 | semidirect |
| 7. #22577397 | C2 | semidirect |
| 8. #22577371 | C2 | semidirect |
| 9. #419×C137 | C2 | semidirect |
| 13. C2×#14555511 | C22 | semidirect |
| 18. C2×Q8×D137 | C22 | semidirect |
| 30. #17984011 | C22 | semidirect |
| 31. #17984008 | C22 | semidirect |
| 32. #17984000 | C22 | semidirect |
| 36. #103×C137 | C22 | semidirect |
| 45. #14555510 | D4 | semidirect |
| 74. C2×Q8×C137 | D4 | semidirect |
| 145. C137 | #3010 | semidirect |
| 153. #419 | D137 | semidirect |
| 180. #103 | C2×D137 | semidirect |
| 200. C2×Q8 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984136 | 2 |
| C2×#17984116 | 2 |
| C22×#14555497 | 2 |
| #22577972 | 2 |
| #22577551 | 2 |
| #22577543 | 2 |
| #22577397 | 2 |
| #22577371 | 2 |
| #419×C137 | 2 |
| #3010 | 137 |