Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22571198 | C2 | semidirect |
| 2. #22570659 | C2 | semidirect |
| 3. #22566316 | C2 | semidirect |
| 4. #22558808 | C2 | semidirect |
| 5. #22558718 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 7. C67×#1555 | C2 | semidirect |
| 41. #14524043 | D4 | semidirect |
| 42. #14524040 | D4 | semidirect |
| 60. #14523954 | D4 | semidirect |
| 73. C4⋊C8×C67 | D4 | semidirect |
| 215. #1555 | D67 | semidirect |
| 219. C67 | #10088 | semidirect |
| 279. C4⋊C8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571198 | 2 |
| #22570659 | 2 |
| #22566316 | 2 |
| #22558808 | 2 |
| #22558718 | 2 |
| #22558101 | 2 |
| C67×#1555 | 2 |
| #10088 | 67 |