Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
644 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 138 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 | C42 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#3567 | C2 |
| LCS | G ▷ C42 ▷ 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×#1521 | C2 | semidirect |
| 3. C23×#1482 | C2 | semidirect |
| 4. C23×#564 | C4 | semidirect |
| 5. C23×#562 | C4 | semidirect |
| 85. #8515 | C23 | direct (N × H) |
| 105. #1521 | C2×C23 | semidirect |
| 106. #1482 | C2×C23 | semidirect |
| 118. #564 | C4×C23 | semidirect |
| 119. #562 | C4×C23 | semidirect |
| 169. C23 | #8515 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3567 | 2 |
| C23×#1521 | 2 |
| C23×#1482 | 2 |
| #8515 | 23 |