Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
524 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C2×C4 | C22×C8×C23 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C23 |
| prime radical | C2×C23×#127 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1459 | C2 | semidirect |
| 3. C23×#1324 | C2 | semidirect |
| 4. C23×#1318 | C2 | semidirect |
| 24. C23×#127 | C8 | semidirect |
| 52. C2×D4×C23 | C2×C8 | semidirect |
| 77. C42×C23 | C2×C8 | semidirect |
| 78. #11479 | C23 | direct (N × H) |
| 118. #1459 | C2×C23 | semidirect |
| 119. #1324 | C2×C23 | semidirect |
| 120. #1318 | C2×C23 | semidirect |
| 170. #127 | C8×C23 | semidirect |
| 187. C23 | #11479 | direct (N × H) |
| 199. C2×D4 | C2×C8×C23 | semidirect |
| 224. C42 | C2×C8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2328 | 2 |
| C23×#1459 | 2 |
| C23×#1324 | 2 |
| C23×#1318 | 2 |
| #11479 | 23 |