Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
164 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22558407 | C2 | semidirect |
| 4. #22558344 | C2 | semidirect |
| 5. C67×#1422 | C2 | semidirect |
| 74. #1422 | D67 | semidirect |
| 77. C67 | #13643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561804 | 2 |
| #22558407 | 2 |
| #22558348 | 2 |
| #22558344 | 2 |
| C67×#1422 | 2 |
| #13643 | 67 |