Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
476 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | #99 |
| commutator | C22×C4 | C2×C8×C23 |
| Frattini, cosocle | C2×#95 | C22×C23 |
| prime radical | C24×C23 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C24×C23 ◁ C2×C23×#95 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C22×Q8×C23 | C8 | semidirect |
| 55. #7131 | C23 | direct (N × H) |
| 132. C22×Q8 | C8×C23 | semidirect |
| 143. C23 | #7131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1446 | 2 |
| C23×#1280 | 2 |
| #7131 | 23 |