Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
670 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 118 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×D4 | C23×C23 |
| prime radical | C22×#41×C23 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×#41×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#1393 | C2 | semidirect |
| 5. C2×C23×#117 | C4 | semidirect |
| 6. C22×C42×C23 | C4 | semidirect |
| 9. C23×#391 | C4 | semidirect |
| 70. #12857 | C23 | direct (N × H) |
| 104. #1393 | C2×C23 | semidirect |
| 124. C2×#117 | C4×C23 | semidirect |
| 125. C22×C42 | C4×C23 | semidirect |
| 128. #391 | C4×C23 | semidirect |
| 161. C23 | #12857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2297 | 2 |
| C23×#1782 | 2 |
| C23×#1393 | 2 |
| #12857 | 23 |