Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
316 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 11. #15692322 | C4 | semidirect |
| 12. C4⋊#11717581 | C4 | semidirect |
| 16. C4⋊#11717579 | C4 | semidirect |
| 17. #15692184 | C4 | semidirect |
| 18. C4⋊C8×C101 | C4 | semidirect |
| 27. C4×#87938 | C8 | semidirect |
| 69. #87938 | C4⋊C8 | direct (N × H) |
| 71. C4×C101 | C4×C8 | semidirect |
| 75. Dic101 | C4×C8 | semidirect |
| 84. C101 | C4×C4⋊C8 | semidirect |
| 101. C4⋊C8 | #87938 | direct (N × H) |
| 159. C4 | C8×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊(C4⋊C8) | 2 |
| C2×C8×#87938 | 2 |
| C42×#87938 | 2 |
| (C2×#87938)⋊C8 | 2 |
| C4⋊C8×D101 | 2 |
| C4×C4⋊C8 | 101 |