Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16863213 | C2 | semidirect |
| 4. #22561124 | C2 | semidirect |
| 6. #22558303 | C2 | semidirect |
| 7. C67×#2151 | C2 | semidirect |
| 155. #2151 | D67 | semidirect |
| 161. C67 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523988 | 2 |
| C2×#16863213 | 2 |
| C2×#16863210 | 2 |
| #22561124 | 2 |
| #22561119 | 2 |
| #22558303 | 2 |
| C67×#2151 | 2 |
| #13440 | 67 |