Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
728 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 728 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 | #1790 |
| commutator | C2×D4 | C22×C4×C23 |
| Frattini, cosocle | C2×#41 | C23×C23 |
| prime radical | C23×#532 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#2123 | C2 | semidirect |
| 4. C23×#1915 | C2 | semidirect |
| 8. C23×#563 | C4 | semidirect |
| 9. C23×#559 | C4 | semidirect |
| 134. #12771 | C23 | direct (N × H) |
| 172. #2123 | C2×C23 | semidirect |
| 173. #1915 | C2×C23 | semidirect |
| 194. #563 | C4×C23 | semidirect |
| 195. #559 | C4×C23 | semidirect |
| 267. C23 | #12771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3550 | 2 |
| C23×#2132 | 2 |
| C23×#2123 | 2 |
| C23×#1915 | 2 |
| C23×#1884 | 2 |
| #12771 | 23 |