Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
628 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 162 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×#99 |
| commutator | C2×C4 | C2×C42×C23 |
| Frattini, cosocle | C22×D4 | C23×C23 |
| prime radical | C2×C23×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C23×#99 | C2 | semidirect |
| 4. C23×#1393 | C2 | semidirect |
| 6. C2×C4×D4×C23 | C4 | semidirect |
| 9. C23×#390 | C4 | semidirect |
| 13. C23×#382 | C4 | semidirect |
| 15. C23×#376 | C4 | semidirect |
| 16. C23×#353 | C4 | semidirect |
| 39. C23×#99 | C2×C4 | semidirect |
| 54. C2×D4×C23 | C42 | semidirect |
| 82. C42×C23 | C42 | semidirect |
| 83. #12628 | C23 | direct (N × H) |
| 126. C4×#99 | C2×C23 | semidirect |
| 127. #1393 | C2×C23 | semidirect |
| 153. C2×C4×D4 | C4×C23 | semidirect |
| 156. #390 | C4×C23 | semidirect |
| 160. #382 | C4×C23 | semidirect |
| 162. #376 | C4×C23 | semidirect |
| 163. #353 | C4×C23 | semidirect |
| 193. #99 | C2×C4×C23 | semidirect |
| 198. C23 | #12628 | direct (N × H) |
| 209. C2×D4 | C42×C23 | semidirect |
| 237. C42 | C42×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2328 | 2 |
| C2×C23×#353 | 2 |
| C4×C23×#99 | 2 |
| C23×#1393 | 2 |
| #12628 | 23 |