Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#15690833 | C2 | semidirect |
| 2. C2×#15690829 | C2 | semidirect |
| 3. #20261166 | C2 | direct (N × H) |
| 4. C2×#15690756 | C2 | semidirect |
| 5. C2×#15690755 | C2 | semidirect |
| 6. C2×#15690751 | C2 | semidirect |
| 7. C2×C16×D97 | C2 | semidirect |
| 8. C2×SD32×C97 | C2 | semidirect |
| 12. #15690833 | C22 | semidirect |
| 14. #15690829 | C22 | semidirect |
| 20. #15690756 | C22 | semidirect |
| 21. #15690755 | C22 | semidirect |
| 22. #15690751 | C22 | semidirect |
| 24. C16×D97 | C22 | semidirect |
| 27. SD32×C97 | C22 | semidirect |
| 95. C2×C97 | #508 | semidirect |
| 100. C97 | C2×#508 | semidirect |
| 106. C2×SD32 | D97 | semidirect |
| 124. SD32 | C2×D97 | semidirect |
| 197. C2 | #20261166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| C2×#15690829 | 2 |
| #20261166 | 2 |
| C2×#15690756 | 2 |
| C2×#15690755 | 2 |
| C2×#15690751 | 2 |
| C2×C16×D97 | 2 |
| C2×SD32×C97 | 2 |
| C2×#508 | 97 |