Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×C22⋊C4 | C23×C23 |
| prime radical | C24×C23 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×#117 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×C4×Q8×C23 | C4 | semidirect |
| 10. C23×#398 | C4 | semidirect |
| 12. C23×#395 | C4 | semidirect |
| 18. C23×#383 | C4 | semidirect |
| 99. #11756 | C23 | direct (N × H) |
| 173. C2×C4×Q8 | C4×C23 | semidirect |
| 177. #398 | C4×C23 | semidirect |
| 179. #395 | C4×C23 | semidirect |
| 185. #383 | C4×C23 | semidirect |
| 232. C23 | #11756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2599 | 2 |
| C23×#1740 | 2 |
| C23×#1464 | 2 |
| C23×#1351 | 2 |
| C23×#1344 | 2 |
| #11756 | 23 |