Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#595 |
| commutator, socle | C22×C17 | C23×C4 |
| Fitting, prime radical | C22×D4×C17 | C4 |
| cosocle | C2×Dic17 | C24 |
| hypercenter | C22×D4 | #595 |
| hypocenter | C17 | #2973 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763840 | C2 | semidirect |
| 2. #11763829 | C2 | semidirect |
| 3. #11763779 | C2 | semidirect |
| 4. C2×C22⋊#3624 | C2 | semidirect |
| 9. C2×#63247 | C22 | semidirect |
| 10. C22×#3624 | C22 | semidirect |
| 18. C22⋊#3624 | C22 | semidirect |
| 19. C22⋊#3624 | C22 | semidirect |
| 20. #10587544 | C22 | semidirect |
| 21. #10587542 | C22 | semidirect |
| 50. C23×C17 | M16 | semidirect |
| 117. C17 | #2973 | semidirect |
| 146. C23 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763840 | 2 |
| #11763829 | 2 |
| #11763779 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×D4×Dic17 | 2 |
| #2973 | 17 |