Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 10. #15690879 | C4 | semidirect |
| 11. #15690864 | C4 | semidirect |
| 15. #15690742 | C4 | semidirect |
| 16. #15690741 | C4 | semidirect |
| 17. #106×C97 | C4 | semidirect |
| 55. C8×C97 | C42 | semidirect |
| 56. #11715895 | C42 | semidirect |
| 76. C97 | #1776 | semidirect |
| 91. #106 | #87604 | semidirect |
| 132. C8 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| C2×#15690864 | 2 |
| C4⋊C4×#87604 | 2 |
| #20261608 | 2 |
| #106×D97 | 2 |
| #1776 | 97 |