Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1886 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 158 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 | #99 |
| commutator | C23 | C22×C8×C23 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C23 |
| prime radical | C26×C23 | C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C24×C23 ◁ C22×C22⋊C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#323 | C2 | semidirect |
| 3. C23×#1316 | C2 | direct (N × H) |
| 13. C23×#323 | C22 | semidirect |
| 21. C25×C23 | C8 | semidirect |
| 72. C24×C23 | C2×C8 | semidirect |
| 92. C2×#1316 | C23 | direct (N × H) |
| 156. C2×#323 | C2×C23 | semidirect |
| 157. #1316 | C2×C23 | direct (N × H) |
| 205. #323 | C22×C23 | semidirect |
| 213. C2×C23 | #1316 | direct (N × H) |
| 223. C25 | C8×C23 | semidirect |
| 242. C23 | C2×#1316 | direct (N × H) |
| 275. C24 | C2×C8×C23 | semidirect |
| 402. C2 | C23×#1316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#379 | 2 |
| C2×C23×#323 | 2 |
| C23×#1316 | 2 |
| C2×#1316 | 23 |