Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
754 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #381 |
| commutator | C24 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C23×D4×C23 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#1306 | C2 | semidirect |
| 50. #8752 | C23 | direct (N × H) |
| 78. #1306 | C2×C23 | semidirect |
| 124. C23 | #8752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2308 | 2 |
| C23×#1783 | 2 |
| C23×#1306 | 2 |
| #8752 | 23 |