Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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. C22×#14524037 | C2 | semidirect |
| 2. #22568283 | C2 | direct (N × H) |
| 3. C2×#16863326 | C2 | semidirect |
| 4. C2×#16863318 | C2 | semidirect |
| 6. C2×#384×C67 | C2 | semidirect |
| 9. C2×#14524037 | C22 | semidirect |
| 14. #16863326 | C22 | semidirect |
| 15. #16863318 | C22 | semidirect |
| 22. #384×C67 | C22 | semidirect |
| 45. C2×C42×C67 | D4 | semidirect |
| 73. C42×C67 | C2×D4 | semidirect |
| 113. C2×C67 | #2823 | semidirect |
| 123. C2×#384 | D67 | semidirect |
| 124. C67 | C2×#2823 | semidirect |
| 138. #384 | C2×D67 | semidirect |
| 161. C2×C42 | D268 | semidirect |
| 191. C42 | C2×D268 | semidirect |
| 231. C2 | #22568283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14524037 | 2 |
| #22568283 | 2 |
| C2×#16863326 | 2 |
| C2×#16863318 | 2 |
| C2×#16863313 | 2 |
| C2×#384×C67 | 2 |
| C2×#2823 | 67 |