Finite Group DatabasebetaFinite Group Databasebeta← C22×(C2×#87604)⋊C4 #27158162
Order 12416.
1880 conjugacy classes of subgroups; only the 634 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 634 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. C2×(C2×#87604)⋊C4 | C2 | direct (N × H) |
| 6. C23×#87604 | C4 | semidirect |
| 8. (C2×#87604)⋊C4 | C22 | direct (N × H) |
| 10. C23×Dic97 | C4 | semidirect |
| 12. C22×C4×D97 | C4 | semidirect |
| 14. C23×C4×C97 | C4 | semidirect |
| 18. C22×#87604 | C2×C4 | semidirect |
| 27. C22×Dic97 | C2×C4 | semidirect |
| 30. C2×C4×D97 | C2×C4 | semidirect |
| 34. C22×C4×C97 | C2×C4 | semidirect |
| 53. C2×#87604 | C22×C4 | semidirect |
| 55. C2×C4×C97 | C22×C4 | semidirect |
| 57. C2×Dic97 | C22×C4 | semidirect |
| 60. C22×C97 | #95 | semidirect |
| 65. C2×D97 | #95 | semidirect |
| 78. C2×C97 | C2×#95 | semidirect |
| 82. D97 | C2×#95 | semidirect |
| 86. C97 | C22×#95 | semidirect |
| 99. C23×C4 | #87604 | semidirect |
| 120. C22×C4 | C2×#87604 | semidirect |
| 145. C2×C4 | C22×#87604 | semidirect |
| 156. C22 | (C2×#87604)⋊C4 | direct (N × H) |
| 167. C2 | C2×(C2×#87604)⋊C4 | 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 |
| C2×(C2×#87604)⋊C4 | 2 |
| C23×C4×D97 | 2 |
| C22×#95 | 97 |