Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
878 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 878 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 | C22×C23 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C23 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3192 | C2 | semidirect |
| 2. C2×C23×#447 | C2 | semidirect |
| 3. C23×#1783 | C2 | semidirect |
| 4. C23×#1471 | C2 | semidirect |
| 5. C23×#1298 | C2 | semidirect |
| 88. #9986 | C23 | direct (N × H) |
| 125. #3192 | C2×C23 | semidirect |
| 126. C2×#447 | C2×C23 | semidirect |
| 127. #1783 | C2×C23 | semidirect |
| 128. #1471 | C2×C23 | semidirect |
| 129. #1298 | C2×C23 | semidirect |
| 199. C23 | #9986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3192 | 2 |
| C2×C23×#447 | 2 |
| C23×#1783 | 2 |
| C23×#1471 | 2 |
| C23×#1298 | 2 |
| #9986 | 23 |