Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C23 |
| prime radical | C23×#3151 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3550 | C2 | semidirect |
| 3. C23×#3138 | C2 | semidirect |
| 4. C23×#1657 | C2 | semidirect |
| 5. C23×#1526 | C2 | semidirect |
| 6. C23×#1525 | C2 | semidirect |
| 8. C23×#563 | C22 | semidirect |
| 27. C23×#330 | C22 | semidirect |
| 28. C23×#329 | C22 | semidirect |
| 116. #19077 | C23 | direct (N × H) |
| 146. #3550 | C2×C23 | semidirect |
| 148. #3138 | C2×C23 | semidirect |
| 149. #1657 | C2×C23 | semidirect |
| 150. #1526 | C2×C23 | semidirect |
| 151. #1525 | C2×C23 | semidirect |
| 168. #563 | C22×C23 | semidirect |
| 187. #330 | C22×C23 | semidirect |
| 188. #329 | C22×C23 | semidirect |
| 238. C23 | #19077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3550 | 2 |
| C23×#3151 | 2 |
| C23×#3138 | 2 |
| C23×#1657 | 2 |
| C23×#1526 | 2 |
| C23×#1525 | 2 |
| #19077 | 23 |