Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 4. #22561000 | C2 | semidirect |
| 5. #22558309 | C2 | semidirect |
| 6. #22558294 | C2 | semidirect |
| 25. #359×C67 | C4 | semidirect |
| 59. C2×C16×C67 | C2×C4 | semidirect |
| 61. #108×C67 | C2×C4 | semidirect |
| 159. C67 | #12949 | semidirect |
| 176. #359 | Dic67 | semidirect |
| 202. C2×C16 | C2×Dic67 | semidirect |
| 207. #108 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569093 | 2 |
| C2×#16863219 | 2 |
| #22561958 | 2 |
| #22561000 | 2 |
| #22558309 | 2 |
| #22558294 | 2 |
| C67×#2143 | 2 |
| #12949 | 67 |