Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#18012765 | C2 | semidirect |
| 2. #23752762 | C2 | semidirect |
| 3. #23752427 | C2 | semidirect |
| 4. #23752417 | C2 | semidirect |
| 5. #23752407 | C2 | semidirect |
| 6. #23752236 | C2 | semidirect |
| 7. #23752211 | C2 | semidirect |
| 8. C2×C4×D4×C151 | C2 | semidirect |
| 14. #18012739 | C22 | semidirect |
| 15. #18012736 | C22 | semidirect |
| 16. #18012727 | C22 | semidirect |
| 21. C4⋊(C151⋊C8) | C22 | semidirect |
| 22. C4⋊(C151⋊C8) | C22 | semidirect |
| 23. #18012662 | C22 | semidirect |
| 24. #18012659 | C22 | semidirect |
| 53. C2×D4×C151 | D4 | semidirect |
| 119. C4×C151 | AGL(1,ℤ/8) | semidirect |
| 129. C151 | #3036 | semidirect |
| 133. C2×C4×D4 | D151 | semidirect |
| 174. C2×D4 | D604 | semidirect |
| 250. C4 | #18012765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| #23752762 | 2 |
| #23752427 | 2 |
| #23752417 | 2 |
| #23752407 | 2 |
| #23752236 | 2 |
| #23752211 | 2 |
| C2×C4×D4×C151 | 2 |
| #3036 | 151 |