Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #22558274 | C2 | semidirect |
| 4. #22558179 | C2 | semidirect |
| 6. #22558130 | C2 | semidirect |
| 7. C67×#1579 | C2 | semidirect |
| 26. #14523986 | C8 | semidirect |
| 54. C67⋊C16 | C2×C8 | semidirect |
| 57. Q16×C67 | C2×C8 | semidirect |
| 105. #1579 | D67 | semidirect |
| 110. C67 | #12065 | semidirect |
| 151. Q16 | C8×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562071 | 2 |
| #22559034 | 2 |
| #22558274 | 2 |
| #22558179 | 2 |
| #22558175 | 2 |
| #22558130 | 2 |
| C67×#1579 | 2 |
| #12065 | 67 |