Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
528 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562120 | C2 | semidirect |
| 2. #22561207 | C2 | semidirect |
| 3. #22558218 | C2 | semidirect |
| 4. #22558133 | C2 | semidirect |
| 5. C67×#3186 | C2 | semidirect |
| 6. C22×D536 | C22 | semidirect |
| 11. C22⋊(C67⋊C16) | C22 | semidirect |
| 12. #16863159 | C22 | semidirect |
| 34. C2×D8×C67 | D4 | semidirect |
| 44. #107×C67 | D4 | semidirect |
| 100. C23×C67 | D16 | semidirect |
| 172. #3186 | D67 | semidirect |
| 177. C67 | #12102 | semidirect |
| 199. C2×D8 | C22⋊D67 | semidirect |
| 215. #107 | C22⋊D67 | semidirect |
| 279. C23 | #14523984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562120 | 2 |
| #22561207 | 2 |
| #22558218 | 2 |
| #22558133 | 2 |
| C67×#3186 | 2 |
| #12102 | 67 |