Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
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. #28417952 | C2 | semidirect |
| 2. #28417943 | C2 | semidirect |
| 3. #28417933 | C2 | semidirect |
| 4. #28417932 | C2 | semidirect |
| 5. #28417932 | C2 | semidirect |
| 6. #28417931 | C2 | semidirect |
| 7. #28417918 | C2 | semidirect |
| 10. C4⋊C4×D467 | C2 | semidirect |
| 11. C2×C4⋊C4×C467 | C2 | semidirect |
| 38. C22⋊D467 | Q8 | semidirect |
| 74. C467 | #554 | semidirect |
| 86. C2×C4⋊C4 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417952 | 2 |
| #28417943 | 2 |
| #28417933 | 2 |
| #28417932 | 2 |
| #28417931 | 2 |
| #28417918 | 2 |
| C4×C22⋊D467 | 2 |
| C4⋊C4×D467 | 2 |
| C2×C4⋊C4×C467 | 2 |
| #554 | 467 |