Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
354 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C23 |
| prime radical | C23×C23 | C2×D8 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×C4⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 80. #12162 | C23 | direct (N × H) |
| 103. C2×C4×C23 | Q32 | semidirect |
| 172. C23 | #12162 | direct (N × H) |
| 229. C2×C4 | C23×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3249 | 2 |
| C23×#2188 | 2 |
| C23×#2056 | 2 |
| C23×#1348 | 2 |
| C23×#1322 | 2 |
| #12162 | 23 |