Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #117 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| socle | C22×C23 | #381 |
| prime radical | C24×C23 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C23×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#1276 | C2 | semidirect |
| 4. C23×#1274 | C2 | semidirect |
| 55. #8733 | C23 | direct (N × H) |
| 80. #1276 | C2×C23 | semidirect |
| 81. #1274 | C2×C23 | semidirect |
| 127. C23 | #8733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2298 | 2 |
| C23×#1458 | 2 |
| C23×#1276 | 2 |
| C23×#1274 | 2 |
| #8733 | 23 |