Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
468 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C2×C4×Q8×C17 | C2 |
| hypercenter | C2×C4×Q8 | D17 |
| hypocenter | C17 | #2568 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. C2×Q8×C17 | Q8 | semidirect |
| 103. C17 | #2568 | semidirect |
| 108. C2×Q8 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| #11762748 | 2 |
| #11762716 | 2 |
| #11762715 | 2 |
| #11762674 | 2 |
| C4×C4⋊Dic17 | 2 |
| C2×C4×Q8×C17 | 2 |
| #2568 | 17 |