Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 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. #22571214 | C2 | semidirect |
| 2. #22570583 | C2 | semidirect |
| 4. #22558808 | C2 | semidirect |
| 5. #22558722 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 7. C67×#1555 | C2 | semidirect |
| 37. #14524043 | D4 | semidirect |
| 38. #14524043 | D4 | semidirect |
| 59. #14523954 | D4 | semidirect |
| 72. C4⋊C8×C67 | D4 | semidirect |
| 204. #1555 | D67 | semidirect |
| 208. C67 | #10096 | semidirect |
| 265. C4⋊C8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571214 | 2 |
| #22570583 | 2 |
| #22566316 | 2 |
| #22558808 | 2 |
| #22558722 | 2 |
| #22558101 | 2 |
| C67×#1555 | 2 |
| #10096 | 67 |