Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#106×D67 | C2 | semidirect |
| 3. C2×#16863206 | C2 | semidirect |
| 4. #22561819 | C2 | semidirect |
| 5. #22558316 | C2 | semidirect |
| 6. #22558315 | C2 | semidirect |
| 7. C2×#360×C67 | C2 | semidirect |
| 12. #16863634 | C4 | semidirect |
| 13. #16863629 | C4 | semidirect |
| 49. #14523977 | C2×C4 | semidirect |
| 52. #14523975 | D4 | semidirect |
| 61. C2×Q16×C67 | C2×C4 | semidirect |
| 63. C2×D8×C67 | C2×C4 | semidirect |
| 70. #106×C67 | D4 | semidirect |
| 175. C2×D67 | #360 | semidirect |
| 195. C2×#360 | D67 | semidirect |
| 199. C67 | #13001 | semidirect |
| 226. C2×Q16 | C4×D67 | semidirect |
| 228. C2×D8 | C4×D67 | semidirect |
| 260. #106 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569786 | 2 |
| C2×#106×D67 | 2 |
| C2×#16863206 | 2 |
| #22561819 | 2 |
| #22558316 | 2 |
| #22558315 | 2 |
| C2×#360×C67 | 2 |
| #13001 | 67 |