Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C23 |
| prime radical | C23×#3549 | C2 |
| LCS | G ▷ 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 |
|---|---|---|
| 2. C23×#3216 | C2 | semidirect |
| 3. C23×#3135 | C2 | semidirect |
| 4. C23×#1659 | C2 | semidirect |
| 5. C23×#1536 | C2 | semidirect |
| 6. C23×#1530 | C2 | semidirect |
| 14. C23×#533 | C22 | semidirect |
| 17. C23×#497 | C22 | semidirect |
| 20. C23×#489 | C22 | semidirect |
| 21. C23×#489 | C22 | semidirect |
| 25. C23×#432 | C22 | semidirect |
| 27. C2×C23×#97 | C22 | semidirect |
| 28. C23×#329 | C22 | semidirect |
| 29. C23×#329 | C22 | semidirect |
| 118. #19056 | C23 | direct (N × H) |
| 151. #3216 | C2×C23 | semidirect |
| 152. #3135 | C2×C23 | semidirect |
| 153. #1659 | C2×C23 | semidirect |
| 154. #1536 | C2×C23 | semidirect |
| 155. #1530 | C2×C23 | semidirect |
| 179. #533 | C22×C23 | semidirect |
| 182. #497 | C22×C23 | semidirect |
| 185. #489 | C22×C23 | semidirect |
| 186. #489 | C22×C23 | semidirect |
| 190. #432 | C22×C23 | semidirect |
| 192. C2×#97 | C22×C23 | semidirect |
| 193. #329 | C22×C23 | semidirect |
| 194. #329 | C22×C23 | semidirect |
| 245. C23 | #19056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3549 | 2 |
| C23×#3216 | 2 |
| C23×#3135 | 2 |
| C23×#1659 | 2 |
| C23×#1536 | 2 |
| C23×#1530 | 2 |
| #19056 | 23 |