Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
556 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, prime radical, cosocle | C23×C17 | C24 |
| Fitting | C17×#384 | C2 |
| hypercenter | #384 | D17 |
| hypocenter | C17 | #2551 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 26. C42×C17 | Q8 | semidirect |
| 28. C4⋊Dic17 | Q8 | semidirect |
| 55. C4×C17 | C4⋊Q8 | semidirect |
| 79. C17 | #2551 | semidirect |
| 93. C42 | Dic34 | semidirect |
| 119. C4 | #10587574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587574 | 2 |
| #11762729 | 2 |
| #11762705 | 2 |
| C4×C4⋊Dic17 | 2 |
| C17×#384 | 2 |
| #2551 | 17 |