Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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 | #393 |
| commutator | C24 | C22×C4×C23 |
| Frattini, cosocle | C25 | C23×C23 |
| prime radical | C25×C23 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C25×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C23×#543 | C4 | semidirect |
| 16. C23×C4×C23 | Q8 | semidirect |
| 33. C2×C22⋊C4×C23 | Q8 | semidirect |
| 65. #11394 | C23 | direct (N × H) |
| 124. #543 | C4×C23 | semidirect |
| 143. C23×C4 | Q8×C23 | semidirect |
| 160. C2×C22⋊C4 | Q8×C23 | semidirect |
| 161. C23 | #11394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#543 | 2 |
| C2×C23×#342 | 2 |
| #11394 | 23 |