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×#16863534 | C2 | semidirect |
| 3. #22560143 | C2 | semidirect |
| 4. #22560119 | C2 | semidirect |
| 10. C22×#11761616 | C22 | semidirect |
| 12. C2×#14523966 | C22 | semidirect |
| 25. C22×Dic134 | D4 | semidirect |
| 61. C24×C67 | SD16 | semidirect |
| 104. Dic134 | #120 | semidirect |
| 114. C22×C67 | #448 | semidirect |
| 133. C67 | #32879 | semidirect |
| 176. C24 | #11761616 | semidirect |
| 242. C22 | #16863534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic134 | 2 |
| C2×#16863534 | 2 |
| #22560143 | 2 |
| #22560119 | 2 |
| C67×#2847 | 2 |
| #32879 | 67 |