Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
500 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | #120 |
| commutator | C42 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C22×D4×C23 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#1847 | C2 | semidirect |
| 5. C23×#1295 | C2 | semidirect |
| 19. C23×#329 | C4 | semidirect |
| 44. C23×#97 | C2×C4 | semidirect |
| 86. #8910 | C23 | direct (N × H) |
| 121. #1847 | C2×C23 | semidirect |
| 123. #1295 | C2×C23 | semidirect |
| 155. #329 | C4×C23 | semidirect |
| 186. #97 | C2×C4×C23 | semidirect |
| 190. C23 | #8910 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2379 | 2 |
| C23×#1959 | 2 |
| C23×#1847 | 2 |
| C2×C23×#329 | 2 |
| C23×#1295 | 2 |
| #8910 | 23 |