Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #28352188 | C2 | semidirect |
| 2. #28352179 | C2 | semidirect |
| 3. #28352169 | C2 | semidirect |
| 4. #28352168 | C2 | semidirect |
| 5. #28352168 | C2 | semidirect |
| 6. #28352167 | C2 | semidirect |
| 7. #28352154 | C2 | semidirect |
| 10. C4⋊C4×D431 | C2 | semidirect |
| 11. C2×C4⋊C4×C431 | C2 | semidirect |
| 38. C22⋊D431 | Q8 | semidirect |
| 74. C431 | #554 | semidirect |
| 86. C2×C4⋊C4 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352188 | 2 |
| #28352179 | 2 |
| #28352169 | 2 |
| #28352168 | 2 |
| #28352167 | 2 |
| #28352154 | 2 |
| C4×C22⋊D431 | 2 |
| C4⋊C4×D431 | 2 |
| C2×C4⋊C4×C431 | 2 |
| #554 | 431 |