Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #123×C179 | C2 |
| hypercenter | #123 | D179 |
| hypocenter | C179 | #540 |
| LCS | G ▷ C22×C179 ▷ C179 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153109 | C2 | semidirect |
| 2. #19153103 | C2 | semidirect |
| 3. #19153098 | C2 | semidirect |
| 4. #19153097 | C2 | semidirect |
| 5. #19153095 | C2 | semidirect |
| 6. #19153088 | C2 | semidirect |
| 7. #19153087 | C2 | semidirect |
| 8. #19153086 | C2 | semidirect |
| 9. #19153086 | C2 | semidirect |
| 10. #19153086 | C2 | semidirect |
| 11. #19153085 | C2 | semidirect |
| 12. C4×C22⋊D179 | C2 | semidirect |
| 13. (C22⋊D179)⋊C4 | C2 | semidirect |
| 14. #19153071 | C2 | semidirect |
| 15. #123×C179 | C2 | semidirect |
| 115. C179 | #540 | semidirect |
| 122. #123 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153109 | 2 |
| #19153103 | 2 |
| #19153098 | 2 |
| #19153097 | 2 |
| #19153095 | 2 |
| #19153088 | 2 |
| #19153087 | 2 |
| #19153086 | 2 |
| #19153085 | 2 |
| C4×C22⋊D179 | 2 |
| (C22⋊D179)⋊C4 | 2 |
| #19153071 | 2 |
| #123×C179 | 2 |
| #540 | 179 |