Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. D97⋊#108 | C2 | semidirect |
| 2. C2×#15690879 | C2 | semidirect |
| 4. #20261614 | C2 | semidirect |
| 16. #15690818 | C4 | semidirect |
| 17. #15690817 | C4 | semidirect |
| 19. #15690816 | C4 | semidirect |
| 24. #131×C97 | C4 | semidirect |
| 116. C97 | #1816 | semidirect |
| 128. #131 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#108 | 2 |
| C2×#15690879 | 2 |
| #20261726 | 2 |
| #20261614 | 2 |
| #131×D97 | 2 |
| #1816 | 97 |