Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15668044 | C2 | semidirect |
| 3. Q8×D356 | C2 | semidirect |
| 4. #19151971 | C2 | semidirect |
| 5. #19151845 | C2 | semidirect |
| 6. #19151808 | C2 | semidirect |
| 7. #19151798 | C2 | semidirect |
| 8. #19151763 | C2 | semidirect |
| 9. #19151738 | C2 | semidirect |
| 10. #19151677 | C2 | semidirect |
| 11. C4×Q16×C89 | C2 | semidirect |
| 72. Q16×C89 | D4 | semidirect |
| 126. C4×C89 | #137 | semidirect |
| 137. C89 | #3278 | semidirect |
| 147. C4×Q16 | D89 | semidirect |
| 197. Q16 | D356 | semidirect |
| 265. C4 | #15668044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668044 | 2 |
| #19152270 | 2 |
| Q8×D356 | 2 |
| #19151971 | 2 |
| #19151845 | 2 |
| #19151808 | 2 |
| #19151798 | 2 |
| #19151763 | 2 |
| #19151738 | 2 |
| #19151677 | 2 |
| C4×Q16×C89 | 2 |
| #3278 | 89 |