Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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×#16863220 | C2 | semidirect |
| 3. #22561945 | C2 | semidirect |
| 4. #22561836 | C2 | semidirect |
| 5. #22560264 | C2 | semidirect |
| 6. #22558315 | C2 | semidirect |
| 7. C67×#2148 | C2 | semidirect |
| 43. #14523983 | D4 | semidirect |
| 181. #2148 | D67 | semidirect |
| 186. C67 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569867 | 2 |
| C2×#16863220 | 2 |
| #22561945 | 2 |
| #22561836 | 2 |
| #22560264 | 2 |
| #22558315 | 2 |
| C67×#2148 | 2 |
| #13400 | 67 |