Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
204 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #327 |
| commutator | C22×C8 | C2×C4×C23 |
| Frattini, cosocle | C2×C4⋊C8 | C22×C23 |
| prime radical | C23×C23 | #102 |
| LCS | G ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×C4⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 49. #7082 | C23 | direct (N × H) |
| 115. C23 | #7082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2056 | 2 |
| C23×#1322 | 2 |
| C23×#1290 | 2 |
| #7082 | 23 |