Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
276 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20261848 | C2 | semidirect |
| 2. C2×C4×#11715906 | C2 | semidirect |
| 3. Q8⋊#11715906 | C2 | semidirect |
| 4. D4⋊#11715906 | C2 | semidirect |
| 44. #13095512 | C8 | semidirect |
| 46. #13095511 | C8 | semidirect |
| 48. #13095510 | C8 | semidirect |
| 54. #41×C97 | C8 | semidirect |
| 69. Q8×C97 | C2×C8 | semidirect |
| 71. D4×C97 | C2×C8 | semidirect |
| 80. D388 | C2×C8 | semidirect |
| 89. Dic194 | C2×C8 | semidirect |
| 119. C97 | #1476 | semidirect |
| 147. #41 | #11715906 | semidirect |
| 178. Q8 | C2×#11715906 | semidirect |
| 185. D4 | C2×#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261848 | 2 |
| C2×C4×#11715906 | 2 |
| Q8⋊#11715906 | 2 |
| D4⋊#11715906 | 2 |
| #41×#87604 | 2 |
| #1476 | 97 |