Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #19151582 | C2 | semidirect |
| 3. C2×#15667928 | C2 | semidirect |
| 4. #19151370 | C2 | semidirect |
| 5. #568×C89 | C2 | semidirect |
| 42. M16×C89 | D4 | semidirect |
| 86. C89 | #1914 | semidirect |
| 87. #568 | D89 | semidirect |
| 123. M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152162 | 2 |
| #19151582 | 2 |
| C2×#15667928 | 2 |
| #19151370 | 2 |
| #568×C89 | 2 |
| #1914 | 89 |