Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #2634 |
| 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 |
|---|---|---|
| 109. C17 | #2634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587556 | 2 |
| #11762748 | 2 |
| #11762747 | 2 |
| #11762739 | 2 |
| #11762728 | 2 |
| #11762693 | 2 |
| #11762677 | 2 |
| C2×C4×Q8×C17 | 2 |
| #2634 | 17 |