Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #23749702 | C2 | semidirect |
| 3. D4×#11924746 | C2 | semidirect |
| 4. #23749375 | C2 | semidirect |
| 5. #23749354 | C2 | semidirect |
| 6. #23749346 | C2 | semidirect |
| 7. D4⋊C8×C149 | C2 | semidirect |
| 55. D4×C149 | M16 | semidirect |
| 83. C149 | #1586 | semidirect |
| 90. D4⋊C8 | D149 | semidirect |
| 131. D4 | #14558719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14558721 | 2 |
| #23749702 | 2 |
| D4×#11924746 | 2 |
| #23749375 | 2 |
| #23749354 | 2 |
| #23749346 | 2 |
| D4⋊C8×C149 | 2 |
| #1586 | 149 |