Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1766 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1766 conjugacy classes of subgroups — too many to draw. Only its 158 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×D4 | C23×C23 |
| prime radical | C22×C23×#127 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C24×C23 ◁ C23×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#353 | C2 | semidirect |
| 3. C23×#1781 | C2 | semidirect |
| 5. C23×D4×C23 | C4 | semidirect |
| 9. C2×C23×#127 | C4 | semidirect |
| 11. C22×C42×C23 | C4 | semidirect |
| 13. C2×C23×#99 | C22 | semidirect |
| 80. C2×D4×C23 | C22⋊C4 | semidirect |
| 96. C42×C23 | C22⋊C4 | semidirect |
| 97. #12693 | C23 | direct (N × H) |
| 146. C2×#353 | C2×C23 | semidirect |
| 147. #1781 | C2×C23 | semidirect |
| 167. C22×C23 | #353 | semidirect |
| 176. C23×D4 | C4×C23 | semidirect |
| 180. C2×#127 | C4×C23 | semidirect |
| 182. C22×C42 | C4×C23 | semidirect |
| 184. C2×#99 | C22×C23 | semidirect |
| 226. C23 | #12693 | direct (N × H) |
| 260. C2×D4 | C22⋊C4×C23 | semidirect |
| 276. C42 | C22⋊C4×C23 | semidirect |
| 343. C22 | C23×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C23×#127 | 2 |
| C2×C23×#353 | 2 |
| C23×#1781 | 2 |
| #12693 | 23 |