Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
926 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 270 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 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C24×C23 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C22×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. #11383 | C23 | direct (N × H) |
| 114. C23 | #11383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C23×#125 | 2 |
| C2×C23×#343 | 2 |
| C23×#1728 | 2 |
| #11383 | 23 |