Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#595 |
| commutator, socle | C2×C17 | C23×C8 |
| Fitting | C17×#131 | C4 |
| prime radical | #41×D17 | C4 |
| cosocle | #3622 | C24 |
| hypercenter | #131 | #595 |
| hypocenter | C17 | #3407 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763868 | C2 | semidirect |
| 2. #11763867 | C2 | semidirect |
| 3. C2×#10587530 | C2 | semidirect |
| 4. #11763865 | C2 | semidirect |
| 13. #10587538 | C22 | semidirect |
| 14. C2×#63216 | C22 | semidirect |
| 17. #10587530 | C22 | semidirect |
| 18. #10587529 | C22 | semidirect |
| 84. C17 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763868 | 2 |
| #11763867 | 2 |
| C2×#10587530 | 2 |
| #11763865 | 2 |
| #131×D17 | 2 |
| #3407 | 17 |