Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
552 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 194 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. C22×#14558746 | C2 | semidirect |
| 2. #23750659 | C2 | direct (N × H) |
| 3. C2×C4⋊#11924753 | C2 | semidirect |
| 4. C2×#18011968 | C2 | semidirect |
| 5. C2×C4×#11924753 | C2 | semidirect |
| 8. C2×#14558746 | C22 | semidirect |
| 12. C4⋊#11924753 | C22 | semidirect |
| 13. #18011968 | C22 | semidirect |
| 14. C4×#11924753 | C22 | semidirect |
| 25. C2×#11924753 | D4 | semidirect |
| 46. #11924753 | C2×D4 | semidirect |
| 63. C2×C4×C149 | M16 | semidirect |
| 75. C4×C149 | C2×M16 | semidirect |
| 80. C2×C149 | #436 | semidirect |
| 85. C149 | C2×#436 | semidirect |
| 146. C2×C4 | #14558746 | semidirect |
| 165. C4 | C2×#14558746 | semidirect |
| 167. C2 | #23750659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558746 | 2 |
| #23750659 | 2 |
| C2×C4⋊#11924753 | 2 |
| C2×#18011968 | 2 |
| C2×C4×#11924753 | 2 |
| C2×#18011873 | 2 |
| C2×#436 | 149 |