Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22570596 | C2 | semidirect |
| 2. #22570309 | C2 | semidirect |
| 4. #22558832 | C2 | semidirect |
| 5. #22558759 | C2 | semidirect |
| 6. #22558653 | C2 | semidirect |
| 7. C67×#1288 | C2 | semidirect |
| 39. #14524043 | D4 | semidirect |
| 40. #14524043 | D4 | semidirect |
| 77. #97×C67 | D4 | semidirect |
| 78. C4×C8×C67 | D4 | semidirect |
| 217. #1288 | D67 | semidirect |
| 218. C67 | #10022 | semidirect |
| 287. #97 | D268 | semidirect |
| 288. C4×C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570596 | 2 |
| #22570309 | 2 |
| #22566064 | 2 |
| #22558832 | 2 |
| #22558759 | 2 |
| #22558653 | 2 |
| C67×#1288 | 2 |
| #10022 | 67 |