Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 398 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. #22561974 | C2 | semidirect |
| 3. #22561926 | C2 | semidirect |
| 4. #22561117 | C2 | semidirect |
| 5. #22561108 | C2 | semidirect |
| 6. #22558323 | C2 | semidirect |
| 7. C67×#2148 | C2 | semidirect |
| 170. #2148 | D67 | semidirect |
| 175. C67 | #13442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863831 | 2 |
| #22561974 | 2 |
| #22561926 | 2 |
| #22561117 | 2 |
| #22561108 | 2 |
| #22558323 | 2 |
| C67×#2148 | 2 |
| #13442 | 67 |