Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 16. C4⋊#11715895 | C4 | semidirect |
| 17. #15690739 | C4 | semidirect |
| 18. C4⋊C8×C97 | C4 | semidirect |
| 79. C4×C97 | #107 | semidirect |
| 83. Dic97 | #107 | semidirect |
| 94. C97 | #1947 | semidirect |
| 111. C4⋊C8 | #87604 | semidirect |
| 177. C4 | #15690879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| #20261681 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261609 | 2 |
| C4⋊C8×D97 | 2 |
| #1947 | 97 |