Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27132776 | C2 | semidirect |
| 3. #27132487 | C2 | semidirect |
| 4. #27132475 | C2 | semidirect |
| 5. #27132473 | C2 | semidirect |
| 6. #27132441 | C2 | semidirect |
| 7. #444×C191 | C2 | semidirect |
| 10. #20259265 | C4 | semidirect |
| 11. #20259263 | C4 | semidirect |
| 28. C191⋊C16 | C2×C4 | semidirect |
| 30. Q16×C191 | C2×C4 | semidirect |
| 32. D8×C191 | C2×C4 | semidirect |
| 68. C191 | AGL(1,ℤ/16) | semidirect |
| 71. #444 | D191 | semidirect |
| 93. Q16 | C4×D191 | semidirect |
| 97. D8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133098 | 2 |
| #27132776 | 2 |
| #27132487 | 2 |
| #27132475 | 2 |
| #27132473 | 2 |
| #27132441 | 2 |
| #444×C191 | 2 |
| AGL(1,ℤ/16) | 191 |