Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 8. #15690871 | C4 | semidirect |
| 13. #15690729 | C4 | semidirect |
| 15. #101×C97 | C4 | semidirect |
| 80. C97 | #1394 | semidirect |
| 93. #101 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#101 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #101×D97 | 2 |
| #1394 | 97 |