Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 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. Q8×#10623494 | C2 | semidirect |
| 3. C8×D356 | C2 | semidirect |
| 4. #19151663 | C2 | semidirect |
| 5. #19151650 | C2 | semidirect |
| 6. C4×C8×D89 | C2 | semidirect |
| 7. C8×Q8×C89 | C2 | semidirect |
| 24. #13083575 | C8 | direct (N × H) |
| 44. Q8×C89 | C2×C8 | semidirect |
| 51. D356 | C2×C8 | semidirect |
| 55. C4×D89 | C2×C8 | semidirect |
| 57. C8×C89 | #41 | semidirect |
| 59. #10623494 | #41 | semidirect |
| 76. C89 | C8×#41 | semidirect |
| 79. C8×Q8 | D89 | semidirect |
| 120. Q8 | C8×D89 | semidirect |
| 135. C8 | #13083575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13083575 | 2 |
| Q8×#10623494 | 2 |
| C8×D356 | 2 |
| #19151663 | 2 |
| #19151650 | 2 |
| C4×C8×D89 | 2 |
| C8×Q8×C89 | 2 |
| C8×#41 | 89 |