Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16863219 | C2 | semidirect |
| 5. #22560999 | C2 | semidirect |
| 6. #22558308 | C2 | semidirect |
| 7. C67×#1378 | C2 | semidirect |
| 21. #16863204 | C4 | semidirect |
| 45. #14523979 | C2×C4 | semidirect |
| 59. C2×C16×C67 | C2×C4 | semidirect |
| 158. #1378 | D67 | semidirect |
| 159. C67 | #12949 | semidirect |
| 202. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569094 | 2 |
| C2×#16863219 | 2 |
| #22561959 | 2 |
| #22561938 | 2 |
| #22560999 | 2 |
| #22558308 | 2 |
| C67×#1378 | 2 |
| #12949 | 67 |