Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
566 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C23 |
| socle | C22×C23 | #392 |
| prime radical | C23×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2399 | C2 | semidirect |
| 4. C23×#1487 | C2 | semidirect |
| 5. C23×#1274 | C2 | semidirect |
| 80. C42×C23 | SD16 | semidirect |
| 84. #10014 | C23 | direct (N × H) |
| 115. #2399 | C2×C23 | semidirect |
| 117. #1487 | C2×C23 | semidirect |
| 118. #1274 | C2×C23 | semidirect |
| 182. C23 | #10014 | direct (N × H) |
| 212. C42 | SD16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3103 | 2 |
| C23×#2399 | 2 |
| C23×#1963 | 2 |
| C23×#1487 | 2 |
| C23×#1274 | 2 |
| #10014 | 23 |