Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 134 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 | #15671548 |
| commutator | C23×#125 | C2×C4 |
| Frattini | #490 | C2×D23 |
| Fitting | C23×#1658 | C2 |
| socle | C2×C23 | #1404 |
| hypercenter | #1658 | D23 |
| hypocenter | C23 | #7524 |
| LCS | G ▷ C23×#125 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1658 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C23×#564 | C4 | semidirect |
| 10. C23×#330 | C4 | semidirect |
| 65. #564 | Dic23 | semidirect |
| 71. #330 | Dic23 | semidirect |
| 88. C23 | #7524 | semidirect |