Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562390 | C2 | semidirect |
| 3. #22562387 | C2 | semidirect |
| 4. #22561634 | C2 | semidirect |
| 5. #22558217 | C2 | semidirect |
| 6. #22558132 | C2 | semidirect |
| 7. C67×#1347 | C2 | semidirect |
| 15. C2×#14523977 | C22 | semidirect |
| 22. C22⋊(C67⋊C16) | C22 | semidirect |
| 25. C22⋊C16×C67 | C22 | semidirect |
| 26. #340×C67 | C22 | semidirect |
| 186. #1347 | D67 | semidirect |
| 188. C67 | #12278 | semidirect |
| 205. C22⋊C16 | C2×D67 | semidirect |
| 207. #340 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570956 | 2 |
| #22562390 | 2 |
| #22562387 | 2 |
| #22561634 | 2 |
| #22558217 | 2 |
| #22558132 | 2 |
| C67×#1347 | 2 |
| #12278 | 67 |