Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
242 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 4. #22558275 | C2 | semidirect |
| 5. #22558274 | C2 | semidirect |
| 6. #22558274 | C2 | semidirect |
| 7. C67×#1368 | C2 | semidirect |
| 28. #14523982 | C8 | semidirect |
| 59. C67⋊C16 | C2×C8 | semidirect |
| 66. C16×C67 | C2×C8 | semidirect |
| 109. #1368 | D67 | semidirect |
| 110. C67 | #12000 | semidirect |
| 169. C16 | C8×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561802 | 2 |
| #22558954 | 2 |
| #334×D67 | 2 |
| #22558275 | 2 |
| #22558274 | 2 |
| C67×#1368 | 2 |
| #12000 | 67 |