Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1212 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C24 | C22×C4×C23 |
| Frattini, cosocle | C25 | C23×C23 |
| prime radical | C23×#2403 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C25×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2308 | C2 | semidirect |
| 3. C23×#1781 | C2 | semidirect |
| 4. C23×#1781 | C2 | semidirect |
| 5. C23×#1304 | C2 | semidirect |
| 9. C2×C23×#120 | C4 | semidirect |
| 16. C23×#386 | C4 | semidirect |
| 21. C25×C23 | C2×C4 | semidirect |
| 36. C23×C4×C23 | C2×C4 | semidirect |
| 51. C2×C22⋊C4×C23 | C2×C4 | semidirect |
| 52. C2×C22⋊C4×C23 | D4 | semidirect |
| 124. #9495 | C23 | direct (N × H) |
| 163. C23×C23 | #99 | semidirect |
| 196. #2308 | C2×C23 | semidirect |
| 197. #1781 | C2×C23 | semidirect |
| 198. #1781 | C2×C23 | semidirect |
| 199. #1304 | C2×C23 | semidirect |
| 244. C2×#120 | C4×C23 | semidirect |
| 251. #386 | C4×C23 | semidirect |
| 266. C25 | C2×C4×C23 | semidirect |
| 281. C23×C4 | C2×C4×C23 | semidirect |
| 296. C2×C22⋊C4 | C2×C4×C23 | semidirect |
| 297. C2×C22⋊C4 | D4×C23 | semidirect |
| 302. C23 | #9495 | direct (N × H) |
| 408. C23 | C23×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2403 | 2 |
| C23×#2308 | 2 |
| C23×#1781 | 2 |
| C23×#1304 | 2 |
| #9495 | 23 |