Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1034 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C23×#2433 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2308 | C2 | semidirect |
| 3. C23×#1783 | C2 | semidirect |
| 4. C23×#1510 | C2 | semidirect |
| 5. C23×#1284 | C2 | semidirect |
| 7. C2×C23×#127 | C4 | semidirect |
| 15. C23×#390 | C4 | semidirect |
| 30. C22×D4×C23 | C2×C4 | semidirect |
| 40. C2×C4⋊C4×C23 | C2×C4 | semidirect |
| 50. C2×C42×C23 | C2×C4 | semidirect |
| 56. C23×#95 | D4 | semidirect |
| 115. #9463 | C23 | direct (N × H) |
| 177. #2308 | C2×C23 | semidirect |
| 178. #1783 | C2×C23 | semidirect |
| 179. #1510 | C2×C23 | semidirect |
| 180. #1284 | C2×C23 | semidirect |
| 218. C2×#127 | C4×C23 | semidirect |
| 226. #390 | C4×C23 | semidirect |
| 250. C22×D4 | C2×C4×C23 | semidirect |
| 260. C2×C4⋊C4 | C2×C4×C23 | semidirect |
| 270. C2×C42 | C2×C4×C23 | semidirect |
| 276. #95 | D4×C23 | semidirect |
| 277. C23 | #9463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2433 | 2 |
| C23×#2308 | 2 |
| C23×#1783 | 2 |
| C23×#1510 | 2 |
| C23×#1284 | 2 |
| #9463 | 23 |