Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
220 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 220 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. #22562111 | C2 | semidirect |
| 3. #22559600 | C2 | semidirect |
| 5. #22558280 | C2 | semidirect |
| 7. C67×#1364 | C2 | semidirect |
| 111. #1364 | D67 | semidirect |
| 113. C67 | #12475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562434 | 2 |
| #22562111 | 2 |
| #22559600 | 2 |
| #22559570 | 2 |
| #22558280 | 2 |
| #22558256 | 2 |
| C67×#1364 | 2 |
| #12475 | 67 |