Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D97⋊#131 | C2 | semidirect |
| 2. #20261804 | C2 | semidirect |
| 3. #20261728 | C2 | semidirect |
| 4. #20261726 | C2 | semidirect |
| 5. #20261725 | C2 | semidirect |
| 6. C2×#15690873 | C2 | semidirect |
| 22. #15690858 | C4 | semidirect |
| 24. #15690857 | C4 | semidirect |
| 25. #15690857 | C4 | semidirect |
| 31. 2−1+4×C97 | C4 | semidirect |
| 45. #13095512 | C2×C4 | semidirect |
| 51. #13095511 | C2×C4 | semidirect |
| 55. #13095510 | C2×C4 | semidirect |
| 59. C2×Dic194 | C2×C4 | semidirect |
| 64. Q8×D97 | C2×C4 | semidirect |
| 75. #41×C97 | C2×C4 | semidirect |
| 77. C2×Q8×C97 | C2×C4 | semidirect |
| 142. C97 | #2898 | semidirect |
| 155. 2−1+4 | #87604 | semidirect |
| 189. #41 | C2×#87604 | semidirect |
| 201. C2×Q8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#131 | 2 |
| #20261804 | 2 |
| #20261728 | 2 |
| #20261726 | 2 |
| #20261725 | 2 |
| C2×#15690873 | 2 |
| 2−1+4×D97 | 2 |
| #2898 | 97 |