Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #22568357 | C2 | semidirect |
| 3. #22559212 | C2 | semidirect |
| 4. #22558239 | C2 | semidirect |
| 5. #22558216 | C2 | semidirect |
| 6. #22558140 | C2 | semidirect |
| 7. C67×#1604 | C2 | semidirect |
| 201. #1604 | D67 | semidirect |
| 205. C67 | #12200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568357 | 2 |
| #22561251 | 2 |
| #22559212 | 2 |
| #22558239 | 2 |
| #22558216 | 2 |
| #22558140 | 2 |
| C67×#1604 | 2 |
| #12200 | 67 |