Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
834 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 150 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 | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#3508 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1965 | C2 | semidirect |
| 3. C23×#1561 | C2 | semidirect |
| 4. C23×#1526 | C2 | semidirect |
| 5. C23×#1489 | C2 | semidirect |
| 103. #8472 | C23 | direct (N × H) |
| 137. #1965 | C2×C23 | semidirect |
| 138. #1561 | C2×C23 | semidirect |
| 139. #1526 | C2×C23 | semidirect |
| 140. #1489 | C2×C23 | semidirect |
| 217. C23 | #8472 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3508 | 2 |
| C23×#1965 | 2 |
| C23×#1561 | 2 |
| C23×#1526 | 2 |
| C23×#1489 | 2 |
| #8472 | 23 |