Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
150 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 46 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 | #1347 |
| commutator | C2×C16 | C2×C4×C23 |
| Frattini, cosocle | C2×M32 | C22×C23 |
| prime radical | C23×#2218 | C2 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C22×C8×C23 ◁ C2×C23×M32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1400 | C2 | semidirect |
| 3. C23×#1384 | C2 | semidirect |
| 4. C2×C23×D16 | C4 | semidirect |
| 9. C23×#367 | C4 | semidirect |
| 40. #7422 | C23 | direct (N × H) |
| 56. #1400 | C2×C23 | semidirect |
| 57. #1384 | C2×C23 | semidirect |
| 69. C2×D16 | C4×C23 | semidirect |
| 74. #367 | C4×C23 | semidirect |
| 93. C23 | #7422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2218 | 2 |
| C23×#1400 | 2 |
| C23×#1384 | 2 |
| #7422 | 23 |