Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
248 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #99 |
| commutator | C2×C4 | C2×C16×C23 |
| Frattini, cosocle | C2×C4⋊C8 | C22×C23 |
| socle | C22×C23 | #323 |
| prime radical | C22×D4×C23 | C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C2×C23×C4⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1322 | C2 | semidirect |
| 25. C2×D4×C23 | C16 | semidirect |
| 44. #7056 | C23 | direct (N × H) |
| 71. #1322 | C2×C23 | semidirect |
| 113. C23 | #7056 | direct (N × H) |
| 118. C2×D4 | C16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1954 | 2 |
| C23×#1322 | 2 |
| #7056 | 23 |