Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#18012767 | C2 | semidirect |
| 2. C2×#18012736 | C2 | semidirect |
| 3. C4×#14559004 | C2 | semidirect |
| 4. #23752413 | C2 | semidirect |
| 5. #23752408 | C2 | semidirect |
| 6. #23752218 | C2 | semidirect |
| 7. #423×C151 | C2 | semidirect |
| 12. C2×#14558993 | C22 | semidirect |
| 13. C2×D1208 | C22 | semidirect |
| 17. C4×Dic302 | C22 | semidirect |
| 18. C4×D604 | C22 | semidirect |
| 23. #18012661 | C22 | semidirect |
| 26. C4⋊C8×C151 | C22 | semidirect |
| 29. #14559004 | D4 | semidirect |
| 62. Dic302 | C2×D4 | semidirect |
| 69. D604 | C2×D4 | semidirect |
| 94. C4×C151 | AGL(1,ℤ/8) | semidirect |
| 104. C151 | #3038 | semidirect |
| 111. #423 | D151 | semidirect |
| 130. C4⋊C8 | C2×D151 | semidirect |
| 201. C4 | #18012767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| C2×#18012736 | 2 |
| C4×#14559004 | 2 |
| #23752413 | 2 |
| #23752408 | 2 |
| #23752218 | 2 |
| #423×C151 | 2 |
| #3038 | 151 |