Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
282 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #329 |
| commutator | C42 | C2×C8×C23 |
| Frattini, cosocle | C2×#97 | C22×C23 |
| prime radical | C2×C23×#127 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1375 | C2 | semidirect |
| 43. #7116 | C23 | direct (N × H) |
| 65. #1375 | C2×C23 | semidirect |
| 104. C23 | #7116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1961 | 2 |
| C23×#1375 | 2 |
| #7116 | 23 |