Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16837840 | C2 | semidirect |
| 2. #21433817 | C2 | semidirect |
| 3. #21433745 | C2 | semidirect |
| 4. C2×#16837214 | C2 | semidirect |
| 5. #21425831 | C2 | semidirect |
| 6. #21425725 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 43. C2×Dic236 | D4 | semidirect |
| 51. C2×D472 | D4 | semidirect |
| 75. M32×C59 | D4 | semidirect |
| 78. #108×C59 | D4 | semidirect |
| 211. #1389 | D59 | semidirect |
| 242. C59 | #13310 | semidirect |
| 283. M32 | D236 | semidirect |
| 287. #108 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837840 | 2 |
| #21433817 | 2 |
| #21433745 | 2 |
| C2×#16837214 | 2 |
| #21425831 | 2 |
| #21425725 | 2 |
| C59×#1389 | 2 |
| #13310 | 59 |