Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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. #15690877 | C4 | semidirect |
| 12. C4⋊#11715897 | C4 | semidirect |
| 16. C4⋊#11715895 | C4 | semidirect |
| 17. #15690739 | C4 | semidirect |
| 18. C4⋊C8×C97 | C4 | semidirect |
| 27. C4×#87604 | C8 | semidirect |
| 69. #87604 | C4⋊C8 | direct (N × H) |
| 71. C4×C97 | C4×C8 | semidirect |
| 75. Dic97 | C4×C8 | semidirect |
| 84. C97 | C4×C4⋊C8 | semidirect |
| 101. C4⋊C8 | #87604 | direct (N × H) |
| 159. C4 | C8×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261736 | 2 |
| C2×C8×#87604 | 2 |
| C42×#87604 | 2 |
| #20261600 | 2 |
| C4⋊C8×D97 | 2 |
| C4×C4⋊C8 | 97 |