Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11763366 | C2 | semidirect |
| 3. #11763174 | C2 | semidirect |
| 4. #11763156 | C2 | semidirect |
| 5. #11762815 | C2 | semidirect |
| 6. C4×M16×C17 | C2 | semidirect |
| 16. #10587556 | C22 | semidirect |
| 17. #10587555 | C22 | semidirect |
| 19. C17×#97 | C22 | semidirect |
| 20. C4×C8×C17 | C22 | semidirect |
| 21. #10587492 | C22 | semidirect |
| 76. C4×M16 | D17 | semidirect |
| 94. #97 | C2×D17 | semidirect |
| 95. C4×C8 | C2×D17 | semidirect |
| 96. C17 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| C2×#10587560 | 2 |
| #11763174 | 2 |
| #11763156 | 2 |
| #11762815 | 2 |
| C4×M16×C17 | 2 |
| #3138 | 17 |