Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17984119 | C2 | semidirect |
| 3. C22×#14555497 | C2 | semidirect |
| 4. C2×#17984096 | C2 | semidirect |
| 5. #22577669 | C2 | direct (N × H) |
| 6. C2×#17984023 | C2 | semidirect |
| 7. C2×#17984004 | C2 | semidirect |
| 8. C2×#101×C137 | C2 | semidirect |
| 12. #17984119 | C22 | semidirect |
| 21. C2×#14555497 | C22 | semidirect |
| 24. #17984096 | C22 | semidirect |
| 29. #17984023 | C22 | semidirect |
| 30. #17984004 | C22 | semidirect |
| 34. #101×C137 | C22 | semidirect |
| 134. C2×C137 | #471 | semidirect |
| 138. C137 | C2×#471 | semidirect |
| 146. C2×#101 | D137 | semidirect |
| 172. #101 | C2×D137 | semidirect |
| 275. C2 | #22577669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| C2×#17984116 | 2 |
| C22×#14555497 | 2 |
| C2×#17984096 | 2 |
| #22577669 | 2 |
| C2×#17984023 | 2 |
| C2×#17984004 | 2 |
| C2×#101×C137 | 2 |
| C2×#471 | 137 |