Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22558553 | C2 | semidirect |
| 3. #22558154 | C2 | semidirect |
| 5. C67×#1467 | C2 | semidirect |
| 179. #1467 | D67 | semidirect |
| 182. C67 | #11534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562916 | 2 |
| #22558553 | 2 |
| #22558154 | 2 |
| #22558140 | 2 |
| C67×#1467 | 2 |
| #11534 | 67 |