Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1232 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 274 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. C22×C4⋊#87604 | C2 | semidirect |
| 4. #20261682 | C2 | direct (N × H) |
| 5. C2×(C2×#87604)⋊C4 | C2 | semidirect |
| 14. C2×C4⋊#87604 | C22 | semidirect |
| 17. (C2×#87604)⋊C4 | C22 | semidirect |
| 20. C2×C22⋊Dic97 | C4 | semidirect |
| 21. C2×#13095488 | C4 | semidirect |
| 22. C22⋊C4×D97 | C4 | semidirect |
| 24. C2×C22⋊C4×C97 | C4 | semidirect |
| 48. C22×Dic97 | C2×C4 | semidirect |
| 51. C2×C4×D97 | C2×C4 | semidirect |
| 53. C22⋊Dic97 | C2×C4 | semidirect |
| 54. #13095488 | C2×C4 | semidirect |
| 56. C22×C4×C97 | C2×C4 | semidirect |
| 57. C22⋊C4×C97 | C2×C4 | semidirect |
| 59. C23×C97 | C4⋊C4 | semidirect |
| 69. C22×D97 | C4⋊C4 | semidirect |
| 70. C22×D97 | C4⋊C4 | semidirect |
| 92. C2×C4×C97 | C22×C4 | semidirect |
| 94. C2×Dic97 | C22×C4 | semidirect |
| 101. C22×C97 | C2×C4⋊C4 | semidirect |
| 111. C2×D97 | C2×C4⋊C4 | semidirect |
| 126. C2×C97 | #385 | semidirect |
| 130. D97 | #385 | semidirect |
| 135. C97 | C2×#385 | semidirect |
| 158. C2×C22⋊C4 | #87604 | semidirect |
| 187. C22×C4 | C2×#87604 | semidirect |
| 192. C22⋊C4 | C2×#87604 | semidirect |
| 212. C23 | C4⋊#87604 | semidirect |
| 232. C2×C4 | C22×#87604 | semidirect |
| 252. C22 | C2×C4⋊#87604 | semidirect |
| 266. C2 | #20261682 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#87604 | 2 |
| C22×C4⋊#87604 | 2 |
| C22×C22⋊#87604 | 2 |
| #20261682 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| C2×C22⋊C4×D97 | 2 |
| C2×#385 | 97 |