Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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, Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#2679 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2094 | C2 | semidirect |
| 3. C23×#1270 | C2 | semidirect |
| 9. C23×#384 | C22 | semidirect |
| 10. C23×#336 | C22 | semidirect |
| 48. #7822 | C23 | direct (N × H) |
| 70. #2094 | C2×C23 | semidirect |
| 71. #1270 | C2×C23 | semidirect |
| 90. #384 | C22×C23 | semidirect |
| 91. #336 | C22×C23 | semidirect |
| 110. C23 | #7822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2679 | 2 |
| C23×#2094 | 2 |
| C23×#1270 | 2 |
| #7822 | 23 |