Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22562488 | C2 | semidirect |
| 3. #22558415 | C2 | semidirect |
| 5. C67×#1422 | C2 | semidirect |
| 70. #1422 | D67 | semidirect |
| 72. C67 | #13709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562488 | 2 |
| #22562091 | 2 |
| #22558415 | 2 |
| #22558397 | 2 |
| C67×#1422 | 2 |
| #13709 | 67 |