Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
518 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
| prime radical | C2×C23×#121 | C22 |
| 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 |
|---|---|---|
| 2. C23×#3095 | C2 | semidirect |
| 4. C23×#1818 | C2 | semidirect |
| 5. C23×#1472 | C2 | semidirect |
| 7. C23×#1293 | C2 | semidirect |
| 132. #9978 | C23 | direct (N × H) |
| 174. #3095 | C2×C23 | semidirect |
| 176. #1818 | C2×C23 | semidirect |
| 177. #1472 | C2×C23 | semidirect |
| 179. #1293 | C2×C23 | semidirect |
| 285. C23 | #9978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3187 | 2 |
| C23×#3095 | 2 |
| C23×#3094 | 2 |
| C23×#1818 | 2 |
| C23×#1472 | 2 |
| C23×#1471 | 2 |
| C23×#1293 | 2 |
| #9978 | 23 |