Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #15690743 | C4 | semidirect |
| 14. #15690741 | C4 | semidirect |
| 15. #15690721 | C4 | semidirect |
| 73. #11715895 | C42 | semidirect |
| 99. C97 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690743 | 2 |
| C2×#15690741 | 2 |
| C2×#15690721 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260497 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #1776 | 97 |