Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 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 |
|---|---|---|
| 1. #22571129 | C2 | semidirect |
| 2. #22571124 | C2 | semidirect |
| 3. #22570654 | C2 | semidirect |
| 4. #22561032 | C2 | semidirect |
| 5. #22558768 | C2 | semidirect |
| 6. #22558053 | C2 | semidirect |
| 7. C67×#1517 | C2 | semidirect |
| 106. C2×C67⋊C8 | D8 | semidirect |
| 218. #1517 | D67 | semidirect |
| 220. C67 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571129 | 2 |
| #22571124 | 2 |
| #22570654 | 2 |
| #22561032 | 2 |
| #22558768 | 2 |
| #22558053 | 2 |
| C67×#1517 | 2 |
| #10218 | 67 |