Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
454 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #393 |
| commutator, Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2862 | C2 | semidirect |
| 4. C23×#1286 | C2 | semidirect |
| 5. C23×#1276 | C2 | semidirect |
| 22. C23×C4⋊Q8 | Q8 | semidirect |
| 23. C23×#127 | Q8 | semidirect |
| 75. #10362 | C23 | direct (N × H) |
| 106. #2862 | C2×C23 | semidirect |
| 109. #1286 | C2×C23 | semidirect |
| 110. #1276 | C2×C23 | semidirect |
| 148. C4⋊Q8 | Q8×C23 | semidirect |
| 149. #127 | Q8×C23 | semidirect |
| 168. C23 | #10362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2862 | 2 |
| C23×#1962 | 2 |
| C23×#1517 | 2 |
| C23×#1286 | 2 |
| C23×#1276 | 2 |
| #10362 | 23 |