Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
142 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15671560 |
| commutator | C4×C8×C23 | C2×C4 |
| Frattini | #492 | C2×D23 |
| Fitting | C23×#1722 | C2 |
| socle | C2×C23 | #1408 |
| hypercenter | #1722 | D23 |
| hypocenter | C23 | #7528 |
| LCS | G ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1722 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C23×#494 | C4 | semidirect |
| 10. C23×#322 | C4 | semidirect |
| 62. #494 | Dic23 | semidirect |
| 67. #322 | Dic23 | semidirect |
| 82. C23 | #7528 | semidirect |