Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
3876 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 3876 conjugacy classes of subgroups — too many to draw. Only its 323 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. C24×Dic134 | C2 | semidirect |
| 2. C2×#16863537 | C2 | semidirect |
| 4. #22560145 | C2 | semidirect |
| 5. C67×#1779 | C2 | semidirect |
| 10. C22×#11761617 | C22 | semidirect |
| 14. C2×#14523968 | C22 | semidirect |
| 25. C22×Dic134 | D4 | semidirect |
| 68. C24×C67 | SD16 | semidirect |
| 104. Dic134 | #120 | semidirect |
| 111. C22×C67 | #448 | semidirect |
| 132. #1779 | D67 | semidirect |
| 133. C67 | #32879 | semidirect |
| 176. C24 | #11761617 | semidirect |
| 242. C22 | #16863537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic134 | 2 |
| C2×#16863537 | 2 |
| #22568491 | 2 |
| #22560145 | 2 |
| C67×#1779 | 2 |
| #32879 | 67 |