Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #22558102 | C2 | semidirect |
| 5. #22558073 | C2 | semidirect |
| 6. #22558065 | C2 | semidirect |
| 7. C67×#2606 | C2 | semidirect |
| 181. #2606 | D67 | semidirect |
| 188. C67 | #10380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561127 | 2 |
| #22558755 | 2 |
| #22558716 | 2 |
| #22558102 | 2 |
| #22558073 | 2 |
| #22558065 | 2 |
| C67×#2606 | 2 |
| #10380 | 67 |