Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20261288 | C2 | semidirect |
| 5. #20260507 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 7. H(3,ℤ/4)×C97 | C2 | semidirect |
| 28. C2×Dic194 | Q8 | semidirect |
| 29. C2×D388 | Q8 | semidirect |
| 103. C97 | #2031 | semidirect |
| 110. H(3,ℤ/4) | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| #20260753 | 2 |
| C2×#15690736 | 2 |
| #20260708 | 2 |
| #20260507 | 2 |
| #20260494 | 2 |
| H(3,ℤ/4)×C97 | 2 |
| #2031 | 97 |