Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19152321 | C2 | semidirect |
| 2. #19151960 | C2 | semidirect |
| 3. #19151950 | C2 | semidirect |
| 4. #19151890 | C2 | semidirect |
| 5. #19151875 | C2 | semidirect |
| 7. #19151803 | C2 | semidirect |
| 8. #19151729 | C2 | semidirect |
| 9. #19151698 | C2 | semidirect |
| 11. D4×Q8×C89 | C2 | semidirect |
| 123. C89 | #3367 | semidirect |
| 125. D4×Q8 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152321 | 2 |
| #19151960 | 2 |
| #19151950 | 2 |
| #19151890 | 2 |
| #19151875 | 2 |
| #19151813 | 2 |
| #19151803 | 2 |
| #19151729 | 2 |
| #19151698 | 2 |
| C4×#13083559 | 2 |
| D4×Q8×C89 | 2 |
| #3367 | 89 |