Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
2594 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 2594 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | #120 |
| commutator | C23 | C2×C42×C23 |
| Frattini, cosocle | C25 | C23×C23 |
| prime radical | C26×C23 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C25×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2273 | C2 | semidirect |
| 3. C2×C23×#342 | C2 | semidirect |
| 9. C23×#379 | C4 | semidirect |
| 48. C24×C23 | C42 | semidirect |
| 59. C22×C4×C23 | C22⋊C4 | semidirect |
| 67. #10935 | C23 | direct (N × H) |
| 108. #2273 | C2×C23 | semidirect |
| 109. C2×#342 | C2×C23 | semidirect |
| 138. #379 | C4×C23 | semidirect |
| 167. C23 | #10935 | direct (N × H) |
| 184. C24 | C42×C23 | semidirect |
| 195. C22×C4 | C22⋊C4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#379 | 2 |
| C23×#2273 | 2 |
| C2×C23×#342 | 2 |
| #10935 | 23 |