Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 181 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×#20259310 | C2 | semidirect |
| 3. C2×#20259301 | C2 | semidirect |
| 4. #27132581 | C2 | semidirect |
| 5. #27132565 | C2 | semidirect |
| 6. #27132518 | C2 | semidirect |
| 7. C4×C22⋊C4×C191 | C2 | semidirect |
| 9. C22×Dic382 | C22 | semidirect |
| 16. C2×C4⋊Dic191 | C22 | semidirect |
| 17. C2×Dic191⋊C4 | C22 | semidirect |
| 19. C2×(C2×D191)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D191)⋊C4 | C22 | semidirect |
| 23. C2×C42×C191 | C22 | semidirect |
| 24. #95×C191 | C22 | semidirect |
| 85. C22×C191 | #124 | semidirect |
| 107. C191 | #2435 | semidirect |
| 115. C4×C22⋊C4 | D191 | semidirect |
| 131. C2×C42 | C2×D191 | semidirect |
| 132. #95 | C2×D191 | semidirect |
| 199. C22 | #20259310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D764 | 2 |
| C2×#20259310 | 2 |
| C2×#20259301 | 2 |
| #27132581 | 2 |
| #27132565 | 2 |
| #27132518 | 2 |
| C4×C22⋊C4×C191 | 2 |
| #2435 | 191 |