Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1244 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 199 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. C4×#14524024 | C2 | semidirect |
| 2. #22561561 | C2 | semidirect |
| 3. #22561457 | C2 | semidirect |
| 4. #22561375 | C2 | semidirect |
| 5. #22561338 | C2 | semidirect |
| 6. C4×#14523958 | C2 | semidirect |
| 78. C22×Dic67 | #41 | semidirect |
| 85. C22⋊Dic67 | #41 | semidirect |
| 196. C67 | #23596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14524024 | 2 |
| #22561561 | 2 |
| #22561457 | 2 |
| #22561375 | 2 |
| #22561338 | 2 |
| C4×#14523958 | 2 |
| C67×#3459 | 2 |
| #23596 | 67 |