Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22561186 | C2 | semidirect |
| 4. #22558897 | C2 | semidirect |
| 6. #22558084 | C2 | semidirect |
| 7. C67×#1831 | C2 | semidirect |
| 114. C42×C67 | SD16 | semidirect |
| 193. #1831 | D67 | semidirect |
| 197. C67 | #10521 | semidirect |
| 304. C42 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571526 | 2 |
| #22561186 | 2 |
| #22561037 | 2 |
| #22558897 | 2 |
| #22558884 | 2 |
| #22558084 | 2 |
| C67×#1831 | 2 |
| #10521 | 67 |