Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14555497 | C2 | semidirect |
| 3. #22577877 | C2 | semidirect |
| 4. #22577615 | C2 | semidirect |
| 5. #22577605 | C2 | semidirect |
| 6. #22577430 | C2 | semidirect |
| 7. #22577412 | C2 | semidirect |
| 8. #22577399 | C2 | semidirect |
| 9. #536×C137 | C2 | semidirect |
| 22. C4⋊#11764040 | C22 | semidirect |
| 23. #17984012 | C22 | semidirect |
| 24. #17984012 | C22 | semidirect |
| 25. #17984009 | C22 | semidirect |
| 28. C4⋊Q8×C137 | C22 | semidirect |
| 29. #124×C137 | C22 | semidirect |
| 116. C137 | #3042 | semidirect |
| 120. #536 | D137 | semidirect |
| 137. C4⋊Q8 | C2×D137 | semidirect |
| 138. #124 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984113 | 2 |
| C22×#14555497 | 2 |
| #22577877 | 2 |
| #22577615 | 2 |
| #22577605 | 2 |
| #22577430 | 2 |
| #22577412 | 2 |
| #22577399 | 2 |
| #536×C137 | 2 |
| #3042 | 137 |