Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×D4×Dic151 | C2 | semidirect |
| 3. C2×#18012701 | C2 | semidirect |
| 4. #23752321 | C2 | direct (N × H) |
| 5. C2×#18012670 | C2 | semidirect |
| 6. C2×#18012661 | C2 | semidirect |
| 7. C2×#18012649 | C2 | semidirect |
| 8. C2×#102×C151 | C2 | semidirect |
| 12. C2×#14558989 | C4 | semidirect |
| 16. D4×Dic151 | C22 | semidirect |
| 18. #18012701 | C22 | semidirect |
| 23. #18012670 | C22 | semidirect |
| 24. #18012661 | C22 | semidirect |
| 25. #18012649 | C22 | semidirect |
| 29. #102×C151 | C22 | semidirect |
| 33. C2×D604 | C2×C4 | semidirect |
| 42. #14558989 | C2×C4 | semidirect |
| 43. C2×C151⋊C8 | C2×C4 | semidirect |
| 54. C2×D4×C151 | C2×C4 | semidirect |
| 68. D604 | C22×C4 | semidirect |
| 77. C151⋊C8 | C22×C4 | semidirect |
| 85. D4×C151 | C22×C4 | semidirect |
| 113. C2×C151 | #442 | semidirect |
| 118. C151 | C2×#442 | semidirect |
| 126. C2×#102 | D151 | semidirect |
| 147. #102 | C2×D151 | semidirect |
| 157. C2×D4 | C4×D151 | semidirect |
| 195. D4 | C2×C4×D151 | semidirect |
| 233. C2 | #23752321 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558989 | 2 |
| C2×D4×Dic151 | 2 |
| C2×#18012701 | 2 |
| #23752321 | 2 |
| C2×#18012670 | 2 |
| C2×#18012661 | 2 |
| C2×#18012649 | 2 |
| C2×#102×C151 | 2 |
| C2×#442 | 151 |