Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #19151645 | C2 | direct (N × H) |
| 4. C2×#15667948 | C2 | semidirect |
| 5. C2×#15667947 | C2 | semidirect |
| 6. C2×#108×C89 | C2 | semidirect |
| 17. #15667948 | C22 | semidirect |
| 18. #15667947 | C22 | semidirect |
| 21. #108×C89 | C22 | semidirect |
| 83. C2×C89 | #430 | semidirect |
| 87. C89 | C2×#430 | semidirect |
| 93. C2×#108 | D89 | semidirect |
| 108. #108 | C2×D89 | semidirect |
| 171. C2 | #19151645 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083557 | 2 |
| C2×M16×D89 | 2 |
| #19151645 | 2 |
| C2×#15667948 | 2 |
| C2×#15667947 | 2 |
| C2×#108×C89 | 2 |
| C2×#430 | 89 |