Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
742 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 742 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 | C23×#3006 | C2 |
| 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×#3187 | C2 | semidirect |
| 2. C23×#3007 | C2 | semidirect |
| 4. C23×#1780 | C2 | semidirect |
| 5. C23×#1472 | C2 | semidirect |
| 6. C23×#1471 | C2 | semidirect |
| 7. C23×#1293 | C2 | semidirect |
| 154. #9975 | C23 | direct (N × H) |
| 211. #3187 | C2×C23 | semidirect |
| 212. #3007 | C2×C23 | semidirect |
| 214. #1780 | C2×C23 | semidirect |
| 215. #1472 | C2×C23 | semidirect |
| 216. #1471 | C2×C23 | semidirect |
| 217. #1293 | C2×C23 | semidirect |
| 332. C23 | #9975 | 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×#3007 | 2 |
| C23×#3006 | 2 |
| C23×#1780 | 2 |
| C23×#1472 | 2 |
| C23×#1471 | 2 |
| C23×#1293 | 2 |
| #9975 | 23 |