Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
456 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #99 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C23 |
| socle | C22×C23 | C2×#99 |
| prime radical | C22×D4×C23 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C23×#1352 | C2 | semidirect |
| 5. C23×#1344 | C2 | semidirect |
| 7. C2×C23×#117 | C4 | semidirect |
| 10. C23×#400 | C4 | semidirect |
| 12. C23×#398 | C4 | semidirect |
| 19. C4×C22⋊C4×C23 | C4 | semidirect |
| 98. #11727 | C23 | direct (N × H) |
| 146. #1352 | C2×C23 | semidirect |
| 147. #1344 | C2×C23 | semidirect |
| 175. C2×#117 | C4×C23 | semidirect |
| 178. #400 | C4×C23 | semidirect |
| 180. #398 | C4×C23 | semidirect |
| 187. C4×C22⋊C4 | C4×C23 | semidirect |
| 232. C23 | #11727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2395 | 2 |
| C4×C23×#99 | 2 |
| C23×#1460 | 2 |
| C23×#1352 | 2 |
| C23×#1344 | 2 |
| #11727 | 23 |