Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22573343 | C2 | semidirect |
| 2. C2×#16863831 | C2 | semidirect |
| 3. #22570695 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. #22561924 | C2 | semidirect |
| 6. #22558295 | C2 | semidirect |
| 7. C67×#1976 | C2 | semidirect |
| 65. #14523983 | D4 | semidirect |
| 67. C2×C67⋊C16 | D4 | semidirect |
| 73. C2×Q16×C67 | D4 | semidirect |
| 75. C2×D8×C67 | D4 | semidirect |
| 223. #1976 | D67 | semidirect |
| 225. C67 | #13334 | semidirect |
| 265. C2×Q16 | D268 | semidirect |
| 277. C2×D8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| C2×#16863831 | 2 |
| #22570695 | 2 |
| #22561944 | 2 |
| #22561924 | 2 |
| #22558295 | 2 |
| C67×#1976 | 2 |
| #13334 | 67 |