Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×#11715871)⋊C4 #27136194
Order 12352.
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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×#11715871)⋊C4 | C2 | direct (N × H) |
| 6. C22×#11715871 | C4 | semidirect |
| 9. C22×Dic193 | C4 | semidirect |
| 11. C2×C4×D193 | C4 | semidirect |
| 13. C22×C4×C193 | C4 | semidirect |
| 17. C2×#11715871 | C2×C4 | semidirect |
| 25. C2×Dic193 | C2×C4 | semidirect |
| 30. C2×C4×C193 | C2×C4 | semidirect |
| 47. C2×C193 | #95 | semidirect |
| 51. D193 | #95 | semidirect |
| 54. C193 | C2×#95 | semidirect |
| 68. C22×C4 | #11715871 | semidirect |
| 85. C2×C4 | C2×#11715871 | semidirect |
| 105. C2 | (C2×#11715871)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715871 | 2 |
| (C2×#11715871)⋊C4 | 2 |
| C22×C4×D193 | 2 |
| C2×#95 | 193 |