Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 17. #10587544 | C4 | semidirect |
| 18. C4⋊#3624 | C4 | semidirect |
| 21. C17×#97 | C4 | semidirect |
| 22. #10587486 | C4 | semidirect |
| 23. #10587486 | C4 | semidirect |
| 24. #10587474 | C4 | semidirect |
| 75. C8×C17 | C4⋊C4 | semidirect |
| 77. #3622 | C4⋊C4 | semidirect |
| 120. #97 | #595 | semidirect |
| 123. C17 | #1771 | semidirect |
| 176. C8 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763810 | 2 |
| C2×#10587532 | 2 |
| C2×C8×#595 | 2 |
| C4×C4⋊#595 | 2 |
| #11763674 | 2 |
| #97×D17 | 2 |
| #1771 | 17 |