Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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×#20259298 | C2 | semidirect |
| 3. #27132582 | C2 | semidirect |
| 4. #27132574 | C2 | semidirect |
| 5. #27132570 | C2 | semidirect |
| 7. #27132536 | C2 | semidirect |
| 8. #27132523 | C2 | semidirect |
| 9. C23×Q8×C191 | C2 | semidirect |
| 34. C2×C22⋊D191 | Q8 | semidirect |
| 55. C2×Q8×C191 | D4 | semidirect |
| 67. C22×D191 | C2×Q8 | semidirect |
| 78. C2×Dic191 | C2×Q8 | semidirect |
| 101. C22×C191 | C22⋊Q8 | semidirect |
| 126. C191 | #2409 | semidirect |
| 128. C23×Q8 | D191 | semidirect |
| 165. C2×Q8 | C22⋊D191 | semidirect |
| 233. C22 | #20259298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259298 | 2 |
| C2×C4×C22⋊D191 | 2 |
| #27132582 | 2 |
| #27132574 | 2 |
| #27132570 | 2 |
| #27132542 | 2 |
| #27132536 | 2 |
| #27132523 | 2 |
| C23×Q8×C191 | 2 |
| #2409 | 191 |