Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16863834 | C2 | semidirect |
| 3. #22570696 | C2 | semidirect |
| 4. #22561924 | C2 | semidirect |
| 5. #22561105 | C2 | semidirect |
| 6. #22558296 | C2 | semidirect |
| 7. C67×#2145 | C2 | semidirect |
| 41. C2×Dic268 | D4 | semidirect |
| 50. C2×D536 | D4 | semidirect |
| 66. C2×C67⋊C16 | D4 | semidirect |
| 82. M32×C67 | D4 | semidirect |
| 221. #2145 | D67 | semidirect |
| 225. C67 | #13334 | semidirect |
| 295. M32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| C2×#16863834 | 2 |
| #22570696 | 2 |
| #22561924 | 2 |
| #22561105 | 2 |
| #22558296 | 2 |
| C67×#2145 | 2 |
| #13334 | 67 |