Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
248 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22562343 | C2 | semidirect |
| 3. #22559095 | C2 | semidirect |
| 4. #22558279 | C2 | semidirect |
| 5. #22558264 | C2 | semidirect |
| 6. #22558255 | C2 | semidirect |
| 7. C67×#1706 | C2 | semidirect |
| 93. C8×C67 | D16 | semidirect |
| 119. #1706 | D67 | semidirect |
| 124. C67 | #12483 | semidirect |
| 211. C8 | #14523984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562343 | 2 |
| #22562241 | 2 |
| #22559095 | 2 |
| #22558279 | 2 |
| #22558264 | 2 |
| #22558255 | 2 |
| C67×#1706 | 2 |
| #12483 | 67 |