Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 9. #15690881 | C4 | semidirect |
| 10. #15690880 | C4 | semidirect |
| 17. #15690746 | C4 | semidirect |
| 18. #15690745 | C4 | semidirect |
| 19. #108×C97 | C4 | semidirect |
| 64. #87604 | #108 | direct (N × H) |
| 74. C97 | C4×#108 | semidirect |
| 89. #108 | #87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#108 | 2 |
| M16×#87604 | 2 |
| C2×C8×#87604 | 2 |
| #20261610 | 2 |
| #108×D97 | 2 |
| C4×#108 | 97 |