Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#15668012 | C2 | semidirect |
| 3. #19151511 | C2 | semidirect |
| 5. #19151464 | C2 | semidirect |
| 6. #19151455 | C2 | semidirect |
| 7. C4×C4⋊C4×C89 | C2 | semidirect |
| 28. C2×D356 | Q8 | semidirect |
| 91. C89 | #2563 | semidirect |
| 98. C4×C4⋊C4 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668012 | 2 |
| C2×C4×D356 | 2 |
| #19151511 | 2 |
| #19151500 | 2 |
| #19151464 | 2 |
| #19151455 | 2 |
| C4×C4⋊C4×C89 | 2 |
| #2563 | 89 |