Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
740 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C23 |
| Frattini, cosocle | C22×Q8 | C23×C23 |
| prime radical | C22×D4×C23 | D4 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C23 ◁ C22×Q8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#356 | C2 | semidirect |
| 5. C23×#1886 | C2 | semidirect |
| 8. C23×#563 | C4 | semidirect |
| 111. #12775 | C23 | direct (N × H) |
| 144. C2×#356 | C2×C23 | semidirect |
| 147. #1886 | C2×C23 | semidirect |
| 166. #563 | C4×C23 | semidirect |
| 226. C23 | #12775 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#563 | 2 |
| C2×C23×#356 | 2 |
| C2×C23×#355 | 2 |
| C23×#1888 | 2 |
| C23×#1886 | 2 |
| #12775 | 23 |