Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
456 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C23 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C43×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 60. #8580 | C23 | direct (N × H) |
| 101. C4×C23 | #330 | semidirect |
| 138. C23 | #8580 | direct (N × H) |
| 199. C4 | C23×#330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C23×#125 | 2 |
| C23×#1767 | 2 |
| C2×C23×#330 | 2 |
| C23×#1295 | 2 |
| #8580 | 23 |