Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
486 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22559942 | C2 | semidirect |
| 3. #22558231 | C2 | semidirect |
| 5. C67×#1464 | C2 | semidirect |
| 6. C2×#14524031 | C4 | semidirect |
| 8. #16863316 | C4 | semidirect |
| 9. #16863313 | C4 | semidirect |
| 16. #16863242 | C4 | semidirect |
| 196. #1464 | D67 | semidirect |
| 199. C67 | #11758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22565896 | 2 |
| #22559942 | 2 |
| #22558231 | 2 |
| #22558207 | 2 |
| C67×#1464 | 2 |
| #11758 | 67 |