Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. #20261746 | C2 | semidirect |
| 4. #20261679 | C2 | semidirect |
| 5. #20261614 | C2 | semidirect |
| 6. #20261606 | C2 | semidirect |
| 25. #15690738 | C4 | semidirect |
| 26. #15690737 | C4 | semidirect |
| 27. #15690736 | C4 | semidirect |
| 28. #104×C97 | C4 | semidirect |
| 57. #13095495 | C2×C4 | semidirect |
| 61. C4×Dic97 | C2×C4 | semidirect |
| 63. M16×C97 | C2×C4 | semidirect |
| 64. C42×C97 | C2×C4 | semidirect |
| 131. C97 | #1860 | semidirect |
| 156. #104 | #87604 | semidirect |
| 179. M16 | C2×#87604 | semidirect |
| 195. C42 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261804 | 2 |
| #20261746 | 2 |
| #20261726 | 2 |
| #20261679 | 2 |
| #20261614 | 2 |
| #20261606 | 2 |
| #104×D97 | 2 |
| #1860 | 97 |