Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
690 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 690 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 | C2×C23 | #1782 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×Q8 | C23×C23 |
| prime radical | C23×#535 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C23×C23 ◁ C23×#519 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2133 | C2 | semidirect |
| 3. C2×C23×#355 | C2 | semidirect |
| 4. C23×#1830 | C2 | semidirect |
| 116. #12729 | C23 | direct (N × H) |
| 148. #2133 | C2×C23 | semidirect |
| 149. C2×#355 | C2×C23 | semidirect |
| 150. #1830 | C2×C23 | semidirect |
| 236. C23 | #12729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3510 | 2 |
| C23×#2133 | 2 |
| C2×C23×#355 | 2 |
| C23×#1830 | 2 |
| #12729 | 23 |