Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
310 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #124 |
| commutator, Frattini, cosocle | C2×C42 | C23×C23 |
| socle | C22×C23 | #397 |
| prime radical | C23×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1832 | C2 | semidirect |
| 4. C23×#1301 | C2 | semidirect |
| 5. C23×#1274 | C2 | semidirect |
| 56. #10629 | C23 | direct (N × H) |
| 79. #1832 | C2×C23 | semidirect |
| 81. #1301 | C2×C23 | semidirect |
| 82. #1274 | C2×C23 | semidirect |
| 126. C23 | #10629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1963 | 2 |
| C23×#1832 | 2 |
| C23×#1540 | 2 |
| C23×#1301 | 2 |
| C23×#1274 | 2 |
| #10629 | 23 |