Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
364 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #99 |
| commutator | C23 | C4×C8×C23 |
| Frattini, cosocle | C2×C4×D4 | C22×C23 |
| socle | C22×C23 | #342 |
| prime radical | C22×D4×C23 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 31. C23×#100 | C8 | semidirect |
| 76. #7203 | C23 | direct (N × H) |
| 176. #100 | C8×C23 | semidirect |
| 183. C23 | #7203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1869 | 2 |
| C4×C23×#100 | 2 |
| C23×#1459 | 2 |
| #7203 | 23 |