Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D191 |
| commutator, socle, cosocle | C23×C191 | C24 |
| Fitting | #393×C191 | C2 |
| prime radical | C22×C22⋊D191 | C22 |
| hypercenter | #393 | D191 |
| hypocenter | C191 | #2398 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic191 | C2 | semidirect |
| 3. #27132605 | C2 | semidirect |
| 4. #27132590 | C2 | semidirect |
| 5. #27132588 | C2 | semidirect |
| 7. #27132574 | C2 | semidirect |
| 8. C22⋊C4×Dic191 | C2 | semidirect |
| 9. #27132510 | C2 | semidirect |
| 10. #27132508 | C2 | semidirect |
| 11. #393×C191 | C2 | semidirect |
| 138. C191 | #2398 | semidirect |
| 147. #393 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic191 | 2 |
| C2×(C22⋊D191)⋊C4 | 2 |
| #27132605 | 2 |
| #27132590 | 2 |
| #27132588 | 2 |
| #27132579 | 2 |
| #27132574 | 2 |
| C22⋊C4×Dic191 | 2 |
| #27132510 | 2 |
| #27132508 | 2 |
| #393×C191 | 2 |
| #2398 | 191 |