Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668006 | C2 | semidirect |
| 2. C2×#15668000 | C2 | semidirect |
| 3. #19151520 | C2 | semidirect |
| 4. #19151519 | C2 | semidirect |
| 5. #19151516 | C2 | semidirect |
| 6. #19151515 | C2 | semidirect |
| 7. #19151511 | C2 | semidirect |
| 9. #19151500 | C2 | semidirect |
| 10. #19151489 | C2 | semidirect |
| 11. C4×C4⋊C4×C89 | C2 | semidirect |
| 70. C42×C89 | D4 | semidirect |
| 144. C89 | #2662 | semidirect |
| 155. C4×C4⋊C4 | D89 | semidirect |
| 214. C42 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668006 | 2 |
| C2×#15668000 | 2 |
| #19151520 | 2 |
| #19151519 | 2 |
| #19151516 | 2 |
| #19151515 | 2 |
| #19151511 | 2 |
| #19151508 | 2 |
| #19151500 | 2 |
| #19151489 | 2 |
| C4×C4⋊C4×C89 | 2 |
| #2662 | 89 |