Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22561814 | C2 | semidirect |
| 4. #22560999 | C2 | semidirect |
| 5. #22558322 | C2 | semidirect |
| 6. #22558320 | C2 | semidirect |
| 14. #16863209 | C4 | semidirect |
| 137. C67 | #13158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863209 | 2 |
| #22561814 | 2 |
| #22560999 | 2 |
| #22558322 | 2 |
| #22558320 | 2 |
| C67×#1978 | 2 |
| #13158 | 67 |