Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
5796 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5796 conjugacy classes of subgroups — too many to draw. Only its 3201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D17 |
| commutator, socle, cosocle | C2×C17 | C26 |
| Fitting | C2×C17×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | D17 |
| hypocenter | C17 | 2−1+6 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763646 | C2 | semidirect |
| 2. #11763645 | C2 | semidirect |
| 3. C2×#10587694 | C2 | semidirect |
| 4. 2−1+4×D17 | C2 | semidirect |
| 5. C2×C17×2−1+4 | C2 | semidirect |
| 6. C17×2−1+4 | C22 | semidirect |
| 7. C2×#41×C17 | C22 | semidirect |
| 8. C22×Q8×C17 | C22 | semidirect |
| 9. #10587697 | C22 | semidirect |
| 10. #10587696 | C22 | semidirect |
| 11. #41×D17 | C22 | semidirect |
| 12. #10587694 | C22 | semidirect |
| 13. #10587694 | C22 | semidirect |
| 14. C2×#63256 | C22 | semidirect |
| 15. C2×Q8×D17 | C22 | semidirect |
| 16. #10587691 | C22 | semidirect |
| 17. C2×#63252 | C22 | semidirect |
| 57. C2×2−1+4 | D17 | semidirect |
| 65. 2−1+4 | C2×D17 | semidirect |
| 71. C2×#41 | C2×D17 | semidirect |
| 73. C22×Q8 | C2×D17 | semidirect |
| 74. C17 | 2−1+6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763646 | 2 |
| #11763645 | 2 |
| C2×#10587694 | 2 |
| 2−1+4×D17 | 2 |
| C2×C17×2−1+4 | 2 |
| 2−1+6 | 17 |