Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569237 | C2 | semidirect |
| 3. #22558923 | C2 | semidirect |
| 4. #22558549 | C2 | semidirect |
| 5. #22558066 | C2 | semidirect |
| 6. #22558064 | C2 | semidirect |
| 7. C67×#1555 | C2 | semidirect |
| 51. C4⋊(C67⋊C8) | D4 | semidirect |
| 68. C4⋊C8×C67 | D4 | semidirect |
| 225. #1555 | D67 | semidirect |
| 229. C67 | #9457 | semidirect |
| 283. C4⋊C8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569237 | 2 |
| #22565156 | 2 |
| #22558923 | 2 |
| #22558549 | 2 |
| #22558066 | 2 |
| #22558064 | 2 |
| C67×#1555 | 2 |
| #9457 | 67 |