Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 15. #15690720 | C4 | semidirect |
| 16. C4×#11715895 | C4 | semidirect |
| 17. C8×Dic97 | C4 | semidirect |
| 18. #97×C97 | C4 | semidirect |
| 73. C97 | #1833 | semidirect |
| 89. #97 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#108 | 2 |
| #20261745 | 2 |
| #20261617 | 2 |
| #20261602 | 2 |
| #20260692 | 2 |
| #1833 | 97 |