Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C4⋊Q8×C373 | C2 |
| prime radical | #26045767 | C2 |
| hypercenter | C4⋊Q8 | D373 |
| hypocenter | C373 | #542 |
| LCS | G ▷ C22×C373 ▷ C373 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26045787 | C2 | semidirect |
| 2. #26045781 | C2 | semidirect |
| 3. #26045780 | C2 | semidirect |
| 4. #26045777 | C2 | semidirect |
| 5. #26045772 | C2 | semidirect |
| 6. #26045768 | C2 | semidirect |
| 8. #26045757 | C2 | semidirect |
| 9. #26045754 | C2 | semidirect |
| 10. #26045749 | C2 | semidirect |
| 11. C4⋊Q8×C373 | C2 | semidirect |
| 73. C373 | #542 | semidirect |
| 75. C4⋊Q8 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045787 | 2 |
| #26045781 | 2 |
| #26045780 | 2 |
| #26045777 | 2 |
| #26045772 | 2 |
| #26045768 | 2 |
| #26045767 | 2 |
| #26045757 | 2 |
| #26045754 | 2 |
| #26045749 | 2 |
| C4⋊Q8×C373 | 2 |
| #542 | 373 |