Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22571208 | C2 | semidirect |
| 3. #22558923 | C2 | semidirect |
| 4. #22558806 | C2 | semidirect |
| 5. #22558721 | C2 | semidirect |
| 6. #22558103 | C2 | semidirect |
| 7. C67×#3138 | C2 | semidirect |
| 47. C4⋊(C67⋊C8) | D4 | semidirect |
| 60. C4⋊Q8×C67 | D4 | semidirect |
| 61. C4⋊Q8×C67 | D4 | semidirect |
| 75. #97×C67 | D4 | semidirect |
| 202. #3138 | D67 | semidirect |
| 208. C67 | #10096 | semidirect |
| 241. C4⋊Q8 | C22⋊D67 | semidirect |
| 242. C4⋊Q8 | C22⋊D67 | semidirect |
| 274. #97 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571208 | 2 |
| #22566316 | 2 |
| #22558923 | 2 |
| #22558806 | 2 |
| #22558721 | 2 |
| #22558103 | 2 |
| C67×#3138 | 2 |
| #10096 | 67 |