Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×#11715906)⋊C4 #27158869
Order 12416.
528 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 191 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×#11715906)⋊C4 | C2 | direct (N × H) |
| 6. C22×#11715906 | C4 | semidirect |
| 17. C2×#11715906 | C2×C4 | semidirect |
| 20. C22×#87604 | C8 | semidirect |
| 31. C22×Dic97 | C8 | semidirect |
| 34. C2×C4×D97 | C8 | semidirect |
| 36. C22×C4×C97 | C8 | semidirect |
| 54. C2×#87604 | C2×C8 | semidirect |
| 61. C2×C4×C97 | C2×C8 | semidirect |
| 63. C2×Dic97 | C2×C8 | semidirect |
| 90. C2×C97 | #336 | semidirect |
| 94. D97 | #336 | semidirect |
| 100. C97 | C2×#336 | semidirect |
| 130. C22×C4 | #11715906 | semidirect |
| 165. C2×C4 | C2×#11715906 | semidirect |
| 195. C2 | (C2×#11715906)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C22×C4×#87604 | 2 |
| C2×#336 | 97 |