Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
290 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #353 |
| commutator | C42 | C42×C23 |
| Frattini, cosocle | C2×#124 | C22×C23 |
| prime radical | C22×D4×C23 | D4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C23 ◁ C22×C4×C23 ◁ C2×C23×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×C23×#97 | C4 | semidirect |
| 10. C23×#384 | C4 | semidirect |
| 12. C23×#355 | C4 | semidirect |
| 14. C23×#354 | C4 | semidirect |
| 70. #7508 | C23 | direct (N × H) |
| 131. C2×#97 | C4×C23 | semidirect |
| 132. #384 | C4×C23 | semidirect |
| 134. #355 | C4×C23 | semidirect |
| 136. #354 | C4×C23 | semidirect |
| 165. C23 | #7508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#355 | 2 |
| C2×C23×#354 | 2 |
| C23×#1959 | 2 |
| #7508 | 23 |