Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D373 |
| commutator, socle, cosocle | C22×C373 | C24 |
| Fitting | #123×C373 | C2 |
| hypercenter | #123 | D373 |
| hypocenter | C373 | #547 |
| LCS | G ▷ C22×C373 ▷ C373 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20238610 | C2 | semidirect |
| 2. C2×#20238609 | C2 | semidirect |
| 3. #26045791 | C2 | semidirect |
| 4. #26045777 | C2 | semidirect |
| 5. #26045776 | C2 | semidirect |
| 6. #26045774 | C2 | semidirect |
| 7. #26045770 | C2 | semidirect |
| 8. #26045769 | C2 | semidirect |
| 9. #26045765 | C2 | semidirect |
| 10. #26045764 | C2 | semidirect |
| 11. #26045752 | C2 | semidirect |
| 12. #26045752 | C2 | semidirect |
| 13. C2×#20238589 | C2 | semidirect |
| 14. C4⋊C4×D373 | C2 | semidirect |
| 15. #123×C373 | C2 | semidirect |
| 61. C22⋊D373 | D4 | semidirect |
| 107. Dic373 | #41 | semidirect |
| 115. C373 | #547 | semidirect |
| 123. #123 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238610 | 2 |
| C2×#20238609 | 2 |
| #26045791 | 2 |
| #26045777 | 2 |
| #26045776 | 2 |
| #26045774 | 2 |
| #26045770 | 2 |
| #26045769 | 2 |
| #26045765 | 2 |
| #26045764 | 2 |
| #26045752 | 2 |
| C2×#20238589 | 2 |
| C4⋊C4×D373 | 2 |
| #123×C373 | 2 |
| #547 | 373 |