Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 137 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. #18011840 | C4 | semidirect |
| 15. C8×Dic149 | C4 | semidirect |
| 65. C8×C149 | C4⋊C4 | semidirect |
| 78. Dic149 | #97 | semidirect |
| 84. C149 | #1770 | semidirect |
| 150. C8 | #14558715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011840 | 2 |
| C2×#18011821 | 2 |
| C2×C8×Dic149 | 2 |
| C4×#14558715 | 2 |
| #23749380 | 2 |
| #23749379 | 2 |
| C2×#97×C149 | 2 |
| #1770 | 149 |