Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
648 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #99 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C23 |
| socle | C22×C23 | C2×#99 |
| prime radical | C23×#2388 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C23×#99 | C2 | semidirect |
| 3. C23×#1460 | C2 | semidirect |
| 4. C23×#1351 | C2 | semidirect |
| 5. C23×#1343 | C2 | semidirect |
| 6. C22×#41×C23 | C4 | semidirect |
| 11. C23×#395 | C4 | semidirect |
| 13. C23×#394 | C4 | semidirect |
| 19. C4×C22⋊C4×C23 | C4 | semidirect |
| 114. #11725 | C23 | direct (N × H) |
| 172. C4×#99 | C2×C23 | semidirect |
| 173. #1460 | C2×C23 | semidirect |
| 174. #1351 | C2×C23 | semidirect |
| 175. #1343 | C2×C23 | semidirect |
| 208. C22×#41 | C4×C23 | semidirect |
| 213. #395 | C4×C23 | semidirect |
| 215. #394 | C4×C23 | semidirect |
| 221. C4×C22⋊C4 | C4×C23 | semidirect |
| 269. C23 | #11725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2388 | 2 |
| C4×C23×#99 | 2 |
| C23×#1460 | 2 |
| C23×#1351 | 2 |
| C23×#1343 | 2 |
| #11725 | 23 |