Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#15667953 | C2 | semidirect |
| 2. C22×#13083549 | C2 | semidirect |
| 3. #19151834 | C2 | semidirect |
| 4. #19151423 | C2 | semidirect |
| 5. #19151399 | C2 | semidirect |
| 6. #19151398 | C2 | semidirect |
| 7. #466×C89 | C2 | semidirect |
| 28. #13083549 | D4 | semidirect |
| 63. C22×C89 | D16 | semidirect |
| 80. C89 | #2215 | semidirect |
| 84. #466 | D89 | semidirect |
| 146. C22 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667953 | 2 |
| C22×#13083549 | 2 |
| #19151834 | 2 |
| #19151423 | 2 |
| #19151399 | 2 |
| #19151398 | 2 |
| #466×C89 | 2 |
| #2215 | 89 |