Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 3. #22561808 | C2 | semidirect |
| 5. #22560997 | C2 | semidirect |
| 6. #22558304 | C2 | semidirect |
| 7. C67×#1389 | C2 | semidirect |
| 15. #16863213 | C4 | semidirect |
| 16. #16863210 | C4 | semidirect |
| 146. #1389 | D67 | semidirect |
| 148. C67 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561959 | 2 |
| C2×#16863202 | 2 |
| #22561808 | 2 |
| #22561105 | 2 |
| #22560997 | 2 |
| #22558304 | 2 |
| C67×#1389 | 2 |
| #13146 | 67 |