Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C2×C4⋊C4×D151 | C2 | semidirect |
| 3. #23752532 | C2 | direct (N × H) |
| 4. C2×#18012670 | C2 | semidirect |
| 5. C2×#18012661 | C2 | semidirect |
| 6. C2×#18012659 | C2 | semidirect |
| 7. C2×(C2×D151)⋊C8 | C2 | semidirect |
| 8. C2×#106×C151 | C2 | semidirect |
| 19. C4⋊C4×D151 | C22 | semidirect |
| 21. #18012670 | C22 | semidirect |
| 22. #18012661 | C22 | semidirect |
| 23. #18012659 | C22 | semidirect |
| 24. (C2×D151)⋊C8 | C22 | semidirect |
| 28. #106×C151 | C22 | semidirect |
| 110. C2×C151 | #481 | semidirect |
| 116. C151 | C2×#481 | semidirect |
| 122. C2×#106 | D151 | semidirect |
| 142. #106 | C2×D151 | semidirect |
| 229. C2 | #23752532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012714 | 2 |
| C2×C4⋊C4×D151 | 2 |
| #23752532 | 2 |
| C2×#18012670 | 2 |
| C2×#18012661 | 2 |
| C2×#18012659 | 2 |
| C2×(C2×D151)⋊C8 | 2 |
| C2×#106×C151 | 2 |
| C2×#481 | 151 |