Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D179 |
| commutator, socle, cosocle | C22×C179 | C24 |
| Fitting | #126×C179 | C2 |
| prime radical | C2×C22⋊D179 | C22 |
| hypercenter | #126 | D179 |
| hypocenter | C179 | #563 |
| LCS | G ▷ C22×C179 ▷ C179 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153113 | C2 | semidirect |
| 2. #19153112 | C2 | semidirect |
| 3. #19153108 | C2 | semidirect |
| 4. #19153107 | C2 | semidirect |
| 5. #19153106 | C2 | semidirect |
| 6. #19153104 | C2 | semidirect |
| 7. #19153103 | C2 | semidirect |
| 11. #19153093 | C2 | semidirect |
| 12. #19153091 | C2 | semidirect |
| 13. #19153090 | C2 | semidirect |
| 14. #19153090 | C2 | semidirect |
| 15. #126×C179 | C2 | semidirect |
| 97. C179 | #563 | semidirect |
| 104. #126 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153113 | 2 |
| #19153112 | 2 |
| #19153108 | 2 |
| #19153107 | 2 |
| #19153106 | 2 |
| #19153104 | 2 |
| #19153103 | 2 |
| #19153099 | 2 |
| #19153097 | 2 |
| #19153095 | 2 |
| #19153093 | 2 |
| #19153091 | 2 |
| #19153090 | 2 |
| #126×C179 | 2 |
| #563 | 179 |