Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #27132570 | C2 | semidirect |
| 3. #27132555 | C2 | semidirect |
| 4. #27132553 | C2 | semidirect |
| 6. C4×(C2×D191)⋊C4 | C2 | semidirect |
| 7. #27132510 | C2 | semidirect |
| 8. #27132508 | C2 | semidirect |
| 9. #391×C191 | C2 | semidirect |
| 12. #20259311 | C4 | semidirect |
| 46. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 47. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 51. C4×Dic191 | C2×C4 | semidirect |
| 54. C2×Q8×C191 | C2×C4 | semidirect |
| 123. C191 | #2372 | semidirect |
| 127. #391 | D191 | semidirect |
| 159. C2×Q8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259311 | 2 |
| #27132570 | 2 |
| #27132555 | 2 |
| #27132553 | 2 |
| #27132541 | 2 |
| C4×(C2×D191)⋊C4 | 2 |
| #27132510 | 2 |
| #27132508 | 2 |
| #391×C191 | 2 |
| #2372 | 191 |