Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
736 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22558332 | C2 | semidirect |
| 4. #22558331 | C2 | semidirect |
| 5. C67×#1392 | C2 | semidirect |
| 213. #1392 | D67 | semidirect |
| 214. C67 | #12579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #413×D67 | 2 |
| #22568651 | 2 |
| #22558332 | 2 |
| #22558331 | 2 |
| C67×#1392 | 2 |
| #12579 | 67 |