Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
410 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 130 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×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C23 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ C2×C4×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 67. #13450 | C23 | direct (N × H) |
| 83. C2×C4×C23 | Q32 | semidirect |
| 148. C23 | #13450 | direct (N × H) |
| 191. C2×C4 | C23×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C23×Q32 | 2 |
| C2×C23×C4⋊C16 | 2 |
| C2×C23×#358 | 2 |
| C23×#1969 | 2 |
| C23×#1380 | 2 |
| #13450 | 23 |