Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
800 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 193 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×#20259320 | C2 | semidirect |
| 4. #27132583 | C2 | semidirect |
| 5. #27132570 | C2 | semidirect |
| 6. #27132569 | C2 | semidirect |
| 9. C2×C4⋊Q8×C191 | C2 | semidirect |
| 55. (C2×D191)⋊C4 | Q8 | semidirect |
| 86. C2×Dic191 | C2×Q8 | semidirect |
| 103. C2×C4×C191 | C2×Q8 | semidirect |
| 113. C2×D191 | C4⋊Q8 | semidirect |
| 128. C191 | #2434 | semidirect |
| 132. C2×C4⋊Q8 | D191 | semidirect |
| 232. C2×C4 | Q8×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D191 | 2 |
| C2×#20259320 | 2 |
| C2×#20259298 | 2 |
| #27132583 | 2 |
| #27132570 | 2 |
| #27132569 | 2 |
| #27132534 | 2 |
| C4×(C2×D191)⋊C4 | 2 |
| C2×C4⋊Q8×C191 | 2 |
| #2434 | 191 |