Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1222 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1222 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 | C22×C23 | #379 |
| commutator | C24 | C22×C4×C23 |
| Frattini, cosocle | C25 | C23×C23 |
| prime radical | C23×D4×C23 | C22 |
| 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×#1819 | C2 | semidirect |
| 4. C23×Q8×C23 | C4 | semidirect |
| 8. C22×C22⋊C4×C23 | C4 | semidirect |
| 10. C22×C42×C23 | C4 | semidirect |
| 71. #8544 | C23 | direct (N × H) |
| 107. #1819 | C2×C23 | semidirect |
| 128. C23×Q8 | C4×C23 | semidirect |
| 132. C22×C22⋊C4 | C4×C23 | semidirect |
| 134. C22×C42 | C4×C23 | semidirect |
| 167. C23 | #8544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C23×#124 | 2 |
| C23×#1819 | 2 |
| C23×#1781 | 2 |
| #8544 | 23 |