Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
324 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C23 |
| prime radical | C23×#2250 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C23×#446 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3402 | C2 | semidirect |
| 3. C23×#2207 | C2 | semidirect |
| 4. C23×#1688 | C2 | semidirect |
| 5. C23×#1360 | C2 | semidirect |
| 6. C23×#1338 | C2 | semidirect |
| 7. C23×#1334 | C2 | semidirect |
| 106. #12337 | C23 | direct (N × H) |
| 135. #3402 | C2×C23 | semidirect |
| 137. #2207 | C2×C23 | semidirect |
| 138. #1688 | C2×C23 | semidirect |
| 139. #1360 | C2×C23 | semidirect |
| 140. #1338 | C2×C23 | semidirect |
| 141. #1334 | C2×C23 | semidirect |
| 218. C23 | #12337 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3402 | 2 |
| C23×#2250 | 2 |
| C23×#2207 | 2 |
| C23×#1688 | 2 |
| C23×#1360 | 2 |
| C23×#1338 | 2 |
| C23×#1334 | 2 |
| #12337 | 23 |