Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
480 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #381 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C22×D4×C23 | D4 |
| LCS | G ▷ C22×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 |
|---|---|---|
| 4. C23×#1297 | C2 | semidirect |
| 5. C23×#1284 | C2 | semidirect |
| 12. C23×#383 | C4 | semidirect |
| 14. C23×#380 | C4 | semidirect |
| 18. C23×#376 | C4 | semidirect |
| 19. C2×C23×#95 | C4 | semidirect |
| 95. #8777 | C23 | direct (N × H) |
| 144. #1297 | C2×C23 | semidirect |
| 145. #1284 | C2×C23 | semidirect |
| 178. #383 | C4×C23 | semidirect |
| 180. #380 | C4×C23 | semidirect |
| 184. #376 | C4×C23 | semidirect |
| 185. C2×#95 | C4×C23 | semidirect |
| 228. C23 | #8777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2353 | 2 |
| C4×C23×#99 | 2 |
| C23×#1465 | 2 |
| C23×#1297 | 2 |
| C23×#1284 | 2 |
| #8777 | 23 |