Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 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. #15690871 | C4 | semidirect |
| 18. #15690729 | C4 | semidirect |
| 19. #15690728 | C4 | semidirect |
| 20. #101×C97 | C4 | semidirect |
| 74. #87604 | #101 | direct (N × H) |
| 85. C97 | C4×#101 | semidirect |
| 103. #101 | #87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87604 | 2 |
| D97⋊#101 | 2 |
| M16×#87604 | 2 |
| #20261614 | 2 |
| #101×D97 | 2 |
| C4×#101 | 97 |