Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153108 | C2 | semidirect |
| 2. #19153103 | C2 | semidirect |
| 3. #19153098 | C2 | semidirect |
| 4. #19153096 | C2 | semidirect |
| 5. #19153092 | C2 | semidirect |
| 6. #19153091 | C2 | semidirect |
| 8. C4×C22⋊D179 | C2 | semidirect |
| 9. C2×C4⋊C4×C179 | C2 | semidirect |
| 66. C179 | #539 | semidirect |
| 76. C2×C4⋊C4 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153108 | 2 |
| #19153103 | 2 |
| #19153098 | 2 |
| #19153096 | 2 |
| #19153092 | 2 |
| #19153091 | 2 |
| #19153087 | 2 |
| C4×C22⋊D179 | 2 |
| C2×C4⋊C4×C179 | 2 |
| #539 | 179 |